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In this chapter, we study the global robust stabilization problem for uncertain nonlinear control systems with the emphasis on systems in the lower triangular form (3.22).

We already investigated in Chap. 7 that, under some suitable assumptions, the GRORP for a given nonlinear system can be converted into a GRSP/GASP for an augmented system. However, the GRSP/GASP itself is a challenging task. So far, the results are mainly limited to nonlinear systems with special structures such as those studied from Chaps. 2 ¿ 6. In this chapter, using the framework established in Chap. 7, we will first study the GRORP for both output feedback systems and lower triangular systems for the case where v(t) ¿ V and w¿ W for two compact sets V and W whose boundary is known, and the exosystem is known exactly. It turns out that, for this case, the GRORP of the output feedback systems and lower triangular systems can be converted to the GRSP of the systems studied in Chap. 4. Then, we will further consider the GRORP for the case where the boundary of V and W is unknown. The chapter is organized as follows. In Sect.¿8.1¿8.3, we study systems with relative degree one, output feedback systems, and lower triangular systems, respectively, under the assumption that the solution of the regulator equations satisfies the nonlinear immersion condition. In Sect.¿8.4, we further consider the GRORP under the assumption that the solution of the regulator equations satisfies the generalized linear immersion condition which allows the exosystem to be nonlinear. In Sect.¿8.5, we consider the GRORP with the boundary of V and W unknown, or what is the same, both the unknown parameter w and the initial state of the exosystem can be arbitrary large. Our approach will be illustrated via the Lorenz system in Sect.¿8.6. Finally, the notes and references are given in Sect.¿8.7.

In this chapter, we review some fundamental concepts and properties of nonlinear control systems that will be referred to in the subsequent chapters.

Attitude control of spacecraft systems has been a benchmark control problem and has been extensively studied under various assumptions and scenarios. When a spacecraft system is subject to external disturbances, the attitude control problem poses some specific challenges. In this chapter, we consider the attitude control problem for a spacecraft subject to a class of external disturbances which is a multi-tone sinusoidal function. The techniques introduced in the previous chapters are integrated to solve this problem. This chapter is organized as follows. In Sects.¿10.1 and 10.2, we present the model of a rigid spacecraft, and formulate the attitude tracking and disturbance rejection problem, respectively. Then a special case where the model of the spacecraft is known exactly is handled in Sect.¿10.3 using the internal model approach studied in Chap. 7. In Sects.¿10.4 and 10.5, taking into account the model uncertainty, we detail the approach to dealing with the attitude control and disturbance rejection problem for the case where the frequencies of the disturbance are known and the case where the frequencies of the disturbance are unknown, respectively. The notes and references are given in Sect.¿10.6.

In this chapter, we study the classification of the affine nonlinear controlsystems of the form (1.10) repeated.

In this section, we summarize some well known results on nonlinear systems without proof. These theorems are cited in Chaps. 2, 3 and 7, respectively.

In Chap. 4, the plant uncertainty, represented by d(t), must be ranged in a compact set D. As a result, a high gain feedback control strategy can be used to dominate uncertainty so that the stability of the closed-loop system is maintained regardless of the change of d(t) as long as d(t) ¿ D for all t= 0.

Having studied the stabilization problem from Chaps. 2 ¿ 6, we now turn to the output regulation problem, or alternatively, servomechanism problem.

In this chapter, we turn to the problem of the global robust output regulation problem with uncertain exosystems. We will still follow the framework established in Chap. 7 to handle this problem.

In Chap. 4, we studied the GRSP for uncertain nonlinear systems containing both dynamic uncertainty and static uncertainty for the case where the boundary of the static uncertainty is known, i.e., d(t) ¿ D for a known compact set D.

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, stability conditions and solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities (LMIs) apart from a small number of scalar parameters that appear nonlinearly. The effectiveness of the proposed control protocol is illustrated by numerical examples.

This paper proposes a switching control strategy for formation maneuvering control of multi-agent systems with guaranteed collision avoidance and connectivity maintenance properties. The control strategy consists of three parts: formation maneuvering, collision avoidance, and connectivity maintenance control. We adopt the idea of using complex Laplacian for formation maneuvering control, which gives rise to one degree of freedom in scaling the size of the achievable formations and thus enables collision avoidance and connectivity maintenance possible in the meantime. Simulation results are provided to demonstrate the effectiveness of the control strategy.

In this paper, a decentralized control algorithm is proposed for a group of vehicles to form diverse collective motion patterns. Without the guidance of a global beacon or a global reference framework, the desired collective behavior occurs provided that the associated network of the multi-vehicle system is jointly-connected. The effectiveness of the approach is verified through theoretical analysis, numerical simulation, and experimental results.

In this paper, we consider consensus of a group of heterogeneous agents with nonlinear dynamics in the presence of system uncertainties. It requires that all agent states reach an agreement which is governed by specified reference dynamics. However, the reference dynamics do not generate a specific reference trajectory for feedback regulation for any agent. For this purpose, the proposed controller integrates two fundamental actions concurrently. On one hand, it asymptotically regulates each individual (heterogeneous, nonlinear, and uncertain) agent dynamics to the common reference dynamics using a generalized robust stabilization technique; on the other hand, it aligns agent trajectories, asymptotically governed by the common reference dynamics, to an agreement through network cooperation. © 2013 IEEE.

The paper presents a linear approach for formation control of multiple autonomous agents in d-dimensional space. The generalized notion of graph Laplacian, associated to a graph with possibly negative weights on the edges, is introduced aiming to solve the formation problem of controlling a network of point agents to form a given pattern (including rotation, translation, and scaling). By assuming the number of agents is larger than d + 1, we derive that a linear distributed control law exists for this purpose if and only if certain algebraic conditions hold (or equivalently, the graph is globally rigid). Next, it is shown that the generalized graph Laplacian used to stabilize the formations can be obtained by solving a convex optimization problem. Further results are also provided to reveal the conditions under which the attained formations are congruent to or just translations of the desired one. © 2013 IEEE.

Chatters are induced by rigidity-flexibility coupling between tools and workpieces, which cause cutting disturbances, over cut and quick tool wear and hence greatly limits the workpiece machining efficiency and quality. To attenuate the chatter dynamics, traditional passive control methods usually decrease the spin speed or cutting depth at the cost of reducing machining efficiency. In this work, we investigate deeply on the structure of the cutting force variation matrix and then design an online system identification method based on the Fourier series. In this way, a Linear Quadratic Regulator adaptive control method is developed to greatly enlarge the chatter stability region in the Lobe Diagram. Moreover, the receding horizon and output rectification mechanisms are applied to overcome the external disturbances as well. The feasibility and superiority of the method are verified by the benchmark examples, where closed-loop stable operation points are remarkably increased and a higher productivity rate is thus achieved. © 2013 Springer-Verlag Berlin Heidelberg.

Some experimental research on flocking of a group of robots in a bounded plane is reported in this paper. The motivation is from many scenarios encountered in both natural systems and engineering applications that collective motions are always confined in a bounded space. Very recently, the conventional flocking formulation and algorithms have been generalized to address the issues caused by bouncing boundaries of a bounded space. In the present experiments, the theoretical design was successfully implemented in a group of real robots such that it achieved a desired rigid flock in a bounded plane. © IFAC.

A robust neural network control scheme for the flexible-joint space robot system with uncertain parameters is discussed in this paper. With linear and angular momentum conservation of the system, the dynamic equations of the robot system are established by the Lagrange method. Then, a kind of joint flexibility compensator is introduced and the singular perturbation approach is utilized to decompose the flexible-joint space robot system into two subsystems. After that, a torque differential feedback controller is given to stabilize the fast subsystem and a robust neural network control scheme is proposed for the slow subsystem to track the expected trajectory in joint space under the effects of uncertain parameters. The convergence of the whole system is analyzed by Lyapunov theorem and verified by the numerical simulations. The theory analysis and simulation results show the feasibility and effectiveness of the proposed control scheme. Copyright © (2012) by the International Astronautical Federation.

The control problem of space-based robot system with uncertain parameters and external disturbances is considered. With Lagrangian formulation and augmentation approach, the dynamic equations of space-based robot system in workspace are derived. Based on the results, an adaptive neural network compensating control scheme for coordinated motion between the base's attitude and end-effector of space-based robot system is developed. It is based on the inertia-related method, and incorporates a neural network controller to compensate the uncertainties. The closed-loop system stability with the neural network adapted on-line is discussed in detail through the Lyapunov stability approach. Comparing with many adaptive and robust control schemes, the controller proposed does not require one to determine the regression matrix for space robot system and then avoids tedious computations. Numerical simulations are provided to show the effectiveness of the approach. Copyright © 2009 by ASME.

In this paper, the coordinated control of a flexible space manipulator system with a front flexible link is discussed. With the assumed mode method and linear momentum conservation of the system, the dynamics of the manpulator is derived in Lagrangian formulation. By using the augmentation approach, a robust control scheme for the coordinated motion between the spacecraft's attitude and arm's joints of the flexible space manipulator with bounded external disturbances and uncertain parameters to track the desired trajectories in joint space is proposed. It is designed based on a priori knowledge about the uncertainty-bound and possesses the advantage that it can greatly reduce the calculation time needed by the adaptive or neural network control schemes. Simulation results show that the presented controller can stabilize the system to track the desired trajectories and keep the vibration amplitude of the flexible arm to be relatively low-level. Copyright © 2010 by ASME.

In this paper, the control problem of space robot system with uncertain parameters and external disturbances is discussed. With the momentum conservation of the system, the kinematics and dynamics of the system are analyzed, and it is found that the generalized Jacobi matrix and the dynamic equations of the system are nonlinearly dependent on inertial parameters. In order to overcome the problems mentioned above, the idea of augmentation approach is introduced. It is shown that the augmented generalized Jacobi matrix and the dynamic equations of the system can be linearly dependent on a group of inertial parameters with augmented inputs and outputs. Based on the results, a robust adaptive composite control scheme for space-based robot to track the desired trajectories in inertial space is developed. The stability of the overall system is analyzed through Lyapunov direct method. For the proposed approach, the global uniform asymptotic stability of the system is established. In addition, the controller presented possesses the advantage that it needs no measurement of the position, linear velocity and acceleration of the base with respect to the orbit, because of the effective exploitation of the particular property of system dynamics. To show the feasibility of control scheme, a planar space robot system is simulated. © 2009 IEEE.

The global robust stabilization problem of cascaded systems with dynamic uncertainties has been approached by the small gain theorem. This method, however, does not produce an explicit Lyapunov function for the closed-loop system. In this paper, we develop a Lyapunov direct method based recursive approach to solve the global robust stabilization problem for the said systems. This method is not only more straightforward than the small gain method, but also produces an explicit Lyapunov function for the closed-loop systems. The Lyapunov function is indispensable when the adaptive control of the same class of systems is further considered. © 2006 IEEE.

The central pattern generator for controlling animal locomotion is generally not a single oscillator but a group of interconnected oscillators. Although the whole group can be analyzed as a bulky single oscillator, it is difficult with such approach to reveal the essential mechanism of phase coordination among oscillators. In this paper, a new approach based on the multivariable harmonic balance is used to analyze a group of identical oscillators that are weakly coupled to each other. Specifically, a lower dimensional matrix representing the coupling structure is abstracted from the overall neuronal connectivity matrix of large dimension, so that the coupling matrix captures the essential mechanism for phase coordination of the oscillators. Moreover, this framework provides an effective way to design the neuronal interconnections to achieve prescribed coordinations among the oscillators. © 2006 IEEE.

The central pattern generator (CPG) is the fundamental mechanism underlying rhythmic movements of animals, and may play important roles in the locomotion control of engineering systems. This paper gives a novel method for synthesizing artificial CPG circuits by utilizing the properties of circulant matrices. The unique feature of the synthesized CPGs is their ability to generate patterns exactly to achieve a prescribed set of frequency, amplitudes, and phases. © 2006 IEEE.

This paper studies the semi-global robust output regulation problem for the class of nonlinear affine systems in normal form. The same problem was studied before by Khalil under the assumption that the solution of the regulator equations is polynomial. By using the nonlinear internal model approach, we have relaxed the polynomial assumption on the solution of the regulator equations. © 2005 AACC.

The solvability of global robust stabilization problem of nonlinear systems by output feedback has been given under various growth conditions on the vector fields of the systems. One of the most common cases is that the vector field is bounded by a linear growth with constant incremental rate. Recently, the problem was solved in for some systems with output dependent incremental rate, without considering the uncertainties. This paper further considers the uncertain systems and gives the robust result.

For over a decade, the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neurally stable. Thus the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions. In this paper, we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems. An example with the well known Van der Pol oscillator as the exosystem is given to illustrate our approach.

The robust servomechanism problem (alternatively, output regulation problem) of the class of nonlinear systems in lower triangular form has been extensively studied in recent years. The semi-global solution was first given by either state feedback or output feedback. The global solution by the state feedback was given very recently. However, the global solution by the output feedback has long been an open problem. In this paper, we present a set of solvability conditions of the global robust servomechanism problem for this class of nonlinear systems by the output feedback control.

The small gain theorem as established in [5] and [6] has been given in terms of a quite general inter-connection of two nonlinear subsystems. This paper gives a more clear-cut version and a more straightforward proof for the small gain theorem for a simpler inter-connection of two nonlinear subsystems by using a different characterization of the ISS concept. Moreover, we have also incorporated some type of model uncertainties into the system description, thus making this special version directly applicable to the global robust stabilization and output regulation problems. © 2004 IEEE.

The global robust servomechanistrl problem (alternatively, global robust output regulation problem) for lower triangular systems has been studied for two special cases. The first case assumes that the systems only contain polynomial nonlinearities, and the second case limits the exogenous signals and the unknown parameters to be within a known bounded set. This paper presents the solvability conditions of the global robust servomechanism problem for the lower triangular systems for the most general case where neither of the above two assumptions is needed. Copyright

We will show that, for the class of nonlinear lower-triangular systems, the robust servomechanism problem can be cast into a robust regulation problem for the same class of systems augmented by dynamic uncertainties. Thus, using our recent result on adaptive regulation of lower-triangular systems with both static and dynamic uncertainties, we will solve the robust servomechanism problem of the lower-triangular systems for the general case where both the uncertain parameter and the exogenous signal can be arbitrarily large. © 2003 IEEE.

While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neurally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we will give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then we will give conditions under which the problem can be converted into a robust stabilization problem of an augmented system. Finally, we will present the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems.

A fundamental limitation to the solvability of the nonlinear robust output regulation problem is a polynomial assumption imposed on the solution of the regulator equations despite over a decade long research on this problem. This assumption is due to the failure of finding an internal model to account for more complex nonlinearities than polynomials. In this paper, we will remove this limitation by constructing a nonlinear internal model.

The regulation problem for cascade connected systems subject to both dynamic and static uncertainties was solved without knowing the bound of the static uncertainty. A technical framework utilizing the dissipativity mechanism was used for the solution of the global regulation problem. The result was shown to be useful for solving other similar problems such as global stabilization problem and servomechanism problem.

A fundamental limitation to the solvability of the nonlinear robust output regulation problem is the polynomial assumption imposed on the solution of the regulator equations. This assumption is due to the failure of finding an internal model to account for more complex nonlinearities than polynomials. Very recently, it was discovered that a nonlinear internal model could be constructed under some assumption much milder than the polynomial assumption. In this paper, we will show that this kind of internal 'model can be used, to solve the global robust output regulation problem for a, class of nonlinear systems in output feedback form.

We study the global output tracking problem for a class of nonlinear cascaded systems coupled with a neutrally stable linear exosystem with uncertain parameters. By extending the stabilization results of cascaded nonlinear systems, and overcoming three major technical obstacles, we have come up with a recursive design procedure that leads to the solution of the problem.

This paper aims to establish a general framework that will convert the robust output regulation problem for nonlinear systems into a robust stabilization problem. This new framework will offer greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling robust output regulation with global stability.

Singular systems are dynamical systems subject to algebraic constraints, and arise in many engineering disciplines. The output regulation problem for singular nonlinear systems has been studied recently for the ideal case where the mathematical model is exactly known. This paper will further consider the robust output regulation problem for a class of singular nonlinear systems which contain uncertain parameters. It will establish the conditions for the solvability of the problem, thus extending the existing results from the normal nonlinear systems to the singular nonlinear systems.

Recently a general framework for studying robust output regulation problem for nonlinear systems is established. This framework is able to convert the robust output regulation problem for nonlinear systems into a robust stabilization problem, thus offering greater flexibility to incorporate recent new stabilization techniques for tackling the global output regulation problem. This paper successfully applies this new framework to solve the global output problem for a class of lower triangular uncertain nonlinear systems.

Autonomous synchronization presents a novel paradigm that circumvents the need for prior knowledge of target agent dynamics in the conventional synchronization of heterogeneous multiagent systems (MASs). It employs a dynamics update law and a state synchronizing control law, collectively termed a two-level controller, to facilitate synchronization in heterogeneous MASs autonomously. Nevertheless, the existing theory is constrained by the requirement of network topology information for calculating sufficiently large gains to design both the dynamics update law and the state synchronizing control law. To overcome this limitation, this article proposes a novel design for the two-level controller, enabling synchronization without reliance on network topology. The design parameters undergo adaptive updates until achieving autonomous synchronization, herein termed adaptive autonomous synchronization.

With advances in network control systems, new applications such as the analysis of opinion dynamics have emerged. Using mathematical tools, various dynamic models have been developed to study how people change opinions in social settings. One such model is the DeGroot-Friedkin model, a two-stage approach for sequential discussion of multiple issues. For each issue, the classical DeGroot model, closely related to the consensus problem, is used to analyze opinion dynamics. This model incorporates the theory of self-appraisal to study the evolution of an individual's self-esteem, where individuals evaluate their contributions to the issues being discussed. However, the question "How does the social network affect one's self-esteem?" remains unaddressed. In this paper, the authors propose a new self-esteem evolution model that examines the effects of social relationships on individuals' self-esteem by considering changes in opinion as an indicator of the social network's impact. The authors also introduce a convergence criterion for the new model and provide analytical proofs of the results.

In this paper, we propose an improved event-triggered control law based on Lyapunov function method for a class of nonlinear systems by integrating a monotonically decreasing dynamics with a reset mechanism at each sampling instance. It is rigorously guaranteed that the sampling interval can be increased compared to a recently designed Lyapunov-function based event-triggered control law when adopted at each step while the advantages compared with other existing event-triggered control laws are maintained. Then, the improved event-triggered law is applied in the adaptive control scheme. Finally, it is verified by numerical examples that the sampling efficiency is improved when the design parameter is appropriately chosen.

This paper investigates the prescribed-time cooperative output regulation (PTCOR) for a class of linear heterogeneous multi-agent systems (MASs) under directed communication graphs. As a special case of PTCOR, the necessary and sufficient condition for prescribed-time output regulation of an individual system is first explored, whereas only sufficient conditions are developed in the literature. A PTCOR algorithm is subsequently developed, composed of prescribed-time distributed observers, local state observers, and tracking controllers, utilizing a distributed feedforward method. This approach converts the PTCOR problem into the prescribed-time stabilization problem of a cascaded subsystem. The criterion for the prescribed-time stabilization of the cascaded system is proposed, differing from that of traditional asymptotic or finite-time stabilization of a cascaded system. It is proven that the regulated outputs converge to zero within a prescribed time and remain at zero afterward, while all internal signals in the closed-loop MASs are uniformly bounded. Finally, the theoretical results are validated through two numerical examples.

This paper presents a novel predefined-time (PDT) event-triggered (ET) optimal bipartite consensus control scheme for multi-agent systems (MASs) with external disturbances. Firstly, an adaptive disturbance observer is designed to accurately estimate the external disturbances within a predefined time, and relax the condition that the upper bound of the disturbance derivative is known. Then, an ET-based consensus optimal control scheme is formulated for MASs by incorporating command filtering technology, backstepping method, and reinforcement learning algorithm. This scheme can obtain satisfactory performance and minimize performance index within a predefined time, and the PDT command filter technique can address "computation complexity" issue. In addition, a new type of dynamic ET mechanism is designed for controller that can ensure the system's PDT stability and reduce the execution time of controller, in which the dynamic variable can achieve PDT convergence. Finally, the practical PDT stability is proved, and the Zeno behavior is excluded. The effectiveness and superiority are validated through simulation examples.

This paper introduces a novel tool based on Lyapunov functions, aimed at analyzing the fixed-time property of networked non-linear uncertain systems while incorporating a specifically designed control law. The applicability of this tool is demonstrated by addressing the fixed-time synchronization challenge within non-linear uncertain multi-agent systems (MASs) operating in a leader-following scenario. In this scenario, the desired trajectory stems from a general non-linear system, and a two-part solution is presented. Both segments of the solution leverage the innovative Lyapunov function-based tool. The first component entails a fixed-time non-linear state feedback observer, engineered to estimate the leader system's state within a directed communication network. The second component offers a fixed-time control law, designed to regulate the trajectories of the agents. This paper explores two categories of non-linear agents with first-order and second-order dynamics, taking into account parametric uncertainties.

A nonparametric learning solution framework is proposed for the global nonlinear robust output regulation problem. We first extend the assumption that the steady-state generator is linear in the exogenous signal to the more relaxed assumption that it is polynomial in the exogenous signal. In addition, a nonparametric learning framework is proposed to eliminate the construction of an explicit regressor, as required in the adaptive method, which can potentially simplify the implementation and reduce the computational complexity of existing methods. With the help of the proposed framework, the robust nonlinear output regulation problem can be converted into a robust nonadaptive stabilization problem for the augmented system with integral input-to-state stable inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. Furthermore, we apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without the need for adaptive parametric techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. Finally, a feedforward control design is proposed to solve the linear output regulation problem using the nonparametric learning framework. Two simulation examples are provided to illustrate the effectiveness of the theoretical results.

In this article, we address the event-triggered consensus problem for single-integrator multiagent systems by introducing a novel nonlinear control protocol. With the proposed consensus protocol, convergence with prescribed transient performance of the closed-loop system can be guaranteed while control execution is triggered by a delicately designed edge-based event-triggering mechanism. The protocol also ensures that no agent exhibits Zeno behavior. Moreover, the method can be extended to the design of a self-triggered algorithm that is able to determine the triggering time sequence without continuously accessing the network states.

The air braking system is crucial for the safe operation of high-speed trains but is susceptible to faults from harsh environments and prolonged use. However, faulty data in practice are still rare because of the "safety oriented principle". For this purpose, fault injection is regularly employed. Due to the stochastic nature of faults in the system, random fault injection can more realistically simulate faulty scenarios compared to the deterministic fault injection. The traditional method entails analyzing a significant amount of raw data to extract the fault distribution function, followed by random sampling. However, the obstacles lie in the scarcity of raw fault data and the labor-intensive nature of constructing the fault distribution function. This paper proposes a layered random fault injection method based on multiple Markov chains. First, a multi-layer structured fault model base is established for the system, followed by the implementation of layered fault injection. Then, the random fault types and degrees are realized using Markov chains, in which the fault probability function is determined by the state transition matrix. Subsequently, a low-complexity Alias sampling algorithm is proposed for discrete random sampling. The nominal model is transformed into a corresponding fault model based on the sampling outcomes, facilitating the acquisition of fault data. Finally, a graphical user interface is developed to present and visualize the validation results.

Belt conveyor systems are essential in industries like automotive, aerospace, power generation, and heavy machinery, with idlers playing a crucial role in ensuring the smooth movement of materials. However, constant operation in noisy environments accelerates wear and tear on idlers and obscures early signs of malfunction, such as grinding or rattling from loose parts. This challenge makes early fault detection difficult, increasing downtime and maintenance costs. Therefore, timely and accurate fault detection is vital to prevent severe system issues, ensure optimal performance, and avoid unexpected breakdowns and costly production interruptions. Intelligent fault detection (IFD) using artificial intelligence (AI) methods has emerged as a solution, with machine learning techniques like convolutional neural networks (CNNs) proving effective. This study uses Yet another Audio Mobilenet Network (YAMNet), initially designed for sound event detection (SED), to identify faults in belt conveyor idlers by analyzing their unique acoustic signatures. We enhance detection capabilities by extracting temporal features from YAMNet-generated embeddings using bidirectional long-term memory (BiLSTM) and bidirectional gated recurrent units (BiGRUs), augmented with a soft attention mechanism. These features are evaluated using extreme gradient boosting (XGBoost), achieving an impressive 90% accuracy in fault detection across idler test sets. Our approach was rigorously compared to the VGGish model and validated on the publicly available malfunctioning industrial machine investigation and inspection (MIMII) dataset, where it demonstrated superior performance with AUC scores of 0.8355 for fans, 0.9414 for pumps, 0.9265 for valves, and 0.9703 for sliders. These results significantly improve over baseline scores, with increases of 19.36% for fans, 38.44% for pumps, 67.26% for valves, and 38.61% for sliders. This advancement represents a significant step forward in conveyor system diagnostics, providing a robust solution for enhancing industrial safety and operational efficiency.

In this article, the global event-triggered (ET) funnel tracking control problem is studied for a class of switched nonlinear systems with structural uncertainties, where the solvability of the control problem for each subsystem is not needed. A switching multiple Lyapunov functions (MLFs) method is established, where MLFs are designed to handle switched inverse dynamics, and a switching barrier Lyapunov function is constructed to address switched sampled errors that may compromise system stability. This is achieved alongside a new switching dynamic event-triggering mechanism (DETM). By combining this method with backstepping, a dwell-time state-dependent switching law and an ET funnel controller of each subsystem are constructed, effectively eliminating the issue of the 'explosion of complexity' encountered in traditional backstepping without using dynamic surface control or command filters. Additionally, the designed switching DETM ensures that the tracking error always evolves within a performance funnel in any consecutive triggering interval, excluding Zeno behavior, and guaranteeing positive constant lower bounds for two consecutive triggering intervals and any switching interval, respectively. Finally, an example is provided to show the validity of the theoretical results.

In this article, we study a data-driven control method for the robust output regulation problem. The method exploits the parameterization property of a system from the observed data that do not necessarily satisfy the persistently exciting condition for system identification. It is based on a data informativity theory, which infers a system property for designing a controller for a whole family of systems (including the true system) that can generate the same observed data. The new idea is to explore the necessary and/or sufficient conditions for the data being informative for transmission zeros, stabilizability, and augmented stabilizability, which can be integrated to derive the conditions for data informativity for robust output regulation. Moreover, under these conditions, a dynamic state feedback data-driven controller is explicitly designed for achieving output regulation with robustness against variation of system matrices and noise in observed data.

This note investigates the consensus of discrete-time multiagent systems, where the consensus error between neighboring agents is subject to transient performance constraints. The examination of transient performance constraints holds paramount importance in ensuring the secure and optimal functioning of real systems. Nevertheless, the existing body of research pertaining to constraints has predominantly focused on continuous-time systems, with limited attention given to discrete-time systems. To address this gap, we propose a novel transformation method capable of converting the consensus error constraint into an input constraint, leading to the development of an effective controller. Consequently, we successfully solve the consensus problem for discrete-time multiagent systems with transient consensus error constraints, marking the first instance of its accomplishment.

Achieving global input-to-state stability (ISS) in closed-loop systems becomes a challenging task when integrating an adaptive scheme into control design. This challenge is particularly prominent in the global output regulation of nonlinear systems. The current state-of-the-art in global robust adaptive output regulators is limited to achieving a weaker form of integral-ISS. In this paper, we present an ISS-based design framework for a class of nonlinear systems with input perturbation via a novel adaptive output regulator. Specifically, we introduce a new adaptive internal model comprising an internal model candidate, a parameter estimator, and a filter. This innovative design transforms the original output regulation problem into a robust stabilization problem. We leverage the cyclic small-gain theorem to design a robust stabilizer, ensuring that the resulting closed-loop system achieves global ISS with the perturbation acting as the input.

In this article, we present an event-triggered control law for systems with an unknown control direction, where the adaptation dynamics of the Nussbaum gain are sampled. Specifically, we employ the emulation method and introduce a specific set of sampling errors. This approach enables the design of an event-triggered law without encountering Zeno behavior. Additionally, we introduce a lemma to address the non-integrability issue of the Nussbaum gain dynamics during the event-triggered law design. We apply this design philosophy to co-design both the continuous-time controller and the event-triggered law, aiming to achieve the global stabilization of systems with an unknown control direction. Finally, we validate the theoretical results through a numerical example.

This article brings a class of distributed internal model-based observer for followers to estimate a leader's trajectory that is governed by nonlinear dynamics subject to parametric uncertainty in a leader-following network. The observer is valid for jointly connected switching networks. It can be adopted to solve the synchronization problem of a multiagent system through a distributed control architecture composed of an observer and a perturbed output regulator for each agent. The effectiveness of the architecture is rigorously proved for a multiagent system of general nonlinear uncertain heterogeneous dynamics in the sense of asymptotically tracking a leader's trajectory. The design procedure with sufficient conditions is explicitly developed and also demonstrated by numerical simulation.

This paper investigates the robust output regulation problem of uncertain linear systems by using a periodic event-triggered controller. A new type of event triggers based on local sampled signals is proposed to monitor events. An event detector only uses local information, avoiding infinitesimal inter-event times as in some continuous event-triggered schemes. A periodic event-triggered system naturally excludes Zeno behavior as the system operates at discrete-time instants. Convergence of tracking error holds for a class of decreasing triggering positive functions. When exponential functions bound the triggering function, analytical characterization of the relationship among sampling, event triggering, and inter-event behavior is established.

This article addresses the resilient practical cooperative output regulation problem (RPCORP) for multiagent systems subjected to both denial-of-service (DoS) attacks and actuator faults. Fundamentally different from the existing solutions to RPCORPs, the system parameters considered in this article are unknown to each agent, and a novel data-driven control approach is introduced to handle such an issue. The solution starts with developing resilient distributed observers for each follower in the presence of DoS attacks. Then, a resilient communication mechanism and a time-varying sampling period are introduced to, respectively, ensure the neighbor state is available as soon as attacks disappear and to avoid targeted attacks launched by intelligent attackers. Furthermore, a model-based fault-tolerant and resilient controller is designed based on the Lyapunov approach and the output regulation theory. In order to remove the reliance on system parameters, we leverage a new data-driven algorithm to learn controller parameters via the collected data. Rigorous analysis shows that the closed-loop system can resiliently achieve practical cooperative output regulation. Finally, a simulation example is given to illustrate the effectiveness of the achieved results.

LaSalle¿Yoshizawa Theorem is an important tool in guaranteeing convergence of a nonlinear time-varying adaptive system. It claims boundedness and convergence when the derivative of a Lyapunov function is negative semidefinite. For a nonlinear system with an external input, the input-to-state stability (ISS) Lyapunov theorem reveals boundedness of system solutions when the derivative of an ISS Lyapunov function is negative definite with an input term. It is interesting to seek a LaSalle¿Yoshizawa like criterion for a nonlinear system with an external input. An intuitive question is whether a certain boundedness property is guaranteed when the derivative of an ISS Lyapunov function is negative semidefinite with an input term. This technical communique gives a negative answer with a counter-example.

A robust output regulation of a control system aims at disturbance rejection and reference tracking in the presence of uncertainties. Technically, the control design contains two mechanisms: the compensation of nontrivial steady states caused by disturbances and/or reference trajectories and the stabilization of an error system relative to steady states. Feedforward compensation and the internal model (including an approximate integrator) are the two main techniques for the former, while the latter is on a case-by-case basis. This article studies an alternative sliding-mode-based approach that can address the two mechanisms simultaneously, thanks to the new concept of sliding-mode-based output zeroing manifold. This concept bridges the two widely studied areas: robust output regulation and sliding-mode control. The approach is also verified by its application in permanent magnet synchronous motor servo systems.

This article studies the cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our article. Distributed adaptive observers are designed for all follower nodes to simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, where the symmetry of Laplacian matrix does not hold. This is due to two newly developed Lyapunov equations, which solely depend on communication network topologies. Interestingly, using these Lyapunov equations, many results of multiagent systems over undirected graphs can be extended to general directed graphs. Finally, this article also advances the knowledge base of adaptive control systems by providing a main tool in the analysis of parameter convergence for adaptive observers.

This article proposes a distributed controller for a network of agents of second-order dynamics to fence a moving target of unknown velocity within their convex hull. Moreover, the agents form a regular polygon formation and avoid collision during the entire evolution. In the control scheme, the agents are not necessarily labeled and the nearest angle rules are applied. Each controller is composed of the functionalities of estimation of the target's velocity, regulation of distance between the agents and the target, and angle repulsion among agents resulting in an equal distribution. The latter two also guarantee collision avoidance. The asymptotical behavior of the closed-loop system is rigorously analyzed, especially subject to the velocity estimation error. The effectiveness of the controller is also demonstrated by numerical simulation.

In this article, we investigate a moving-target-fencing problem for multiple vehicles using nearest neighbor rules where the target moves with an unknown constant velocity. Without a predefined stand-off distance or formation, two local cooperative controllers are proposed using only the relative position information from the target and its neighbors within its local frame of reference. The controllers consist of three functionalities. The repulsive term between a vehicle and its neighbors is used to avoid collision. The attractive term between a vehicle and the target drives the vehicle toward the target. The adaptive term amounts to estimate the target's velocity. Specifically, with the first controller, the vehicles follow the target's velocity in the average sense resulting in rotation about the target; with the second controller, each vehicle is able to follow the target's velocity resulting in a rigid formation. Furthermore, a decentralized estimator is applied to handle the case where only a portion of vehicles can access the target's position. Both controllers assure target fencing. The results are proved by rigorous theoretical analysis and verified by extensive numerical simulation.

Guided policy search algorithms have been proven to work with incredible accuracy not only for controlling complicated dynamical systems, but also in learning optimal policies from exploration of various unseen instances. This paper deals with a trajectory optimization problem for an unknown dynamical system subject to measurement noise using expectation maximization and extends it to learning (optimal) policies which have less stochasticity in trajectories because of the higher exploitation efficiency. Theoretical and empirical evidence of learned optimal policies for the new approach is depicted in comparison to some well known baselines which are evaluated on an autonomous system with widely used performance metrics.

In this paper, we address the consensus problem for double-integrator multi-agent systems integrated with a novel reset control protocol. It reveals the conditions under which consensus is achieved and the reset function is in action. The proposed reset control essentially provides a dynamically generated higher gain for better transient consensus performance, including faster convergence with less control effort. Compared with a static high gain controller, this dynamic high gain mechanism is more efficient and sophisticated especially in regularly resetting the additional gain to zero during the dynamic evolution.

In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known, and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multiagent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multiagent systems. In this scheme, asymptotic consensus of a second-order uncertain multiagent system is achieved in a network of directed graph.

This article studies the moving-target-fencing problem of multiple second-order vehicles, where the target moves with an unknown constant velocity. Without a predefined stand-off distance or formation, two classes of local cooperative controllers are proposed with and without velocity measurements. Specifically, the first controller uses the relative position information from the target and vehicle's neighbors, as well as the vehicle's velocity measurement, while the second controller relaxes the common requirement of velocity measurement of the vehicles. It is proved that both controllers simultaneously assure target fencing, collision avoidance, and velocity convergence. Finally, numerical simulations are provided to verify the efficacy of the proposed controllers.

Economic dispatch is a critical problem in operation of power grids. A consensus-based algorithm was recently proposed to solve the economic dispatch problem in a distributed manner. In this paper, we propose a novel secure scheme for the consensus-based economic dispatch algorithm using the Paillier cryptosystem. This secure scheme ensures that not only the network transmitted information is protected from external malicious party but also the privacy information of each node remains intact. The proposed secure scheme has two features. First, it relies on the solution to the so-called structural consensus problem with time-varying network weights. Second, it contains a strategy for transmitting encrypted information and generating network weights with randomness, as well as treatment of the practical issues like quantization error and computation overflow/underflow. The performance in terms of cost optimization and privacy-preserving is verified by rigorous theoretical analysis and numerical simulation.

The paper proposes a novel event-triggered control scheme for nonlinear systems. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, it forms a cyclic mapping from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggered law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. Within this framework, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.

We address design, implementation, and characterization of semiconductor strain gauges as stage displacement sensors with small footprint for piezo-driven nanopositioners in differential actuation mode. The strain gauges are not collocated with the stage of the nanopositioner. They are attached to piezo stack actuators in both longitudinal and transverse directions. We address two differential configurations for the displacement sensing. The first configuration uses all strain gauges and provides three output signals. Two of them are proportional to the length variations of the piezo actuators, which are considered as conventional non-differential sensing method. The last output in the first configuration is the first proposed differential sensor. In the second configuration, we propose an alternative differential sensor using only the longitudinal strain gauges and a simpler readout circuit. The results indicate that in the differential actuation mode, a differential sensing strategy provides much better accuracy than the conventional non-differential schemes. Using a laser interferometer as an independent collocated sensor for stage displacement, we obtained constant calibration factors both proposed differential sensors and characterized their sensing accuracies.

This paper aims at secure and privacy-preserving consensus algorithms of networked systems. Due to the technical challenges behind decentralized design of such algorithms, the existing results are mainly restricted to a network of systems with simplest first-order dynamics. Like many other control problems, breakthrough of the gap between first-order dynamics and higher-order ones demands for more advanced technical developments. In this paper, we explore a Paillier encryption based average consensus algorithm for a network of systems with second-order dynamics, with randomness added to network weights. The conditions for privacy-preserving, especially depending on consensus rate, are thoroughly studied with theoretical analysis and numerical verification.

We study a novel piezo-driven nanopositioning mechanism in the horizontal plane. For each horizontal axis, we employ two externally leverage mechanisms with flexure hinges to provide bilateral displacement of the output stage as well as amplified displacement with respect to strokes of two piezo stack actuator. The bilateral amplified motion is achieved by differential actuation of the PZT stack pair of each axis. We also designed a housing structure for the nanopositioner with holes and trenches for safe and neat wiring. It also provides proper installation on the optical table and allows incorporation of auxiliary parts to hold and and align capacitive displacement sensors for precise measurements. We designed wedge mechanisms that together with the housing and the nanopositioner structure allow proper alignment of PZT stacks during installation as well as preloading them. Experiments were carried out to identify the ranges of displacements for the output stage as well as the inputs of the leverage mechanism, using Laser-Doppler-Vibrometry and capacitive sensors. We also developed a simple rigid-link-ideal-hinge kinematic model for the leverage mechanism, which was consistent with the experimental results under no external load conditions. However, due to the external loads and elasticity, large deviations exist between the experimental results and the predicted values by the model. The discrepancy revealed a non-reciprocal property of the individual leverage mechanism and the need to employ more accurate flexure hinge models. Experiments show that the proposed nanopositioner amplifies the input stroke of the PZT stacks by a factor around 12 in the differential actuation mode. Compared to the conventional non-differential actuation modes, the differential one provides almost twice stroke for the output stage as well as more linear input¿output characteristics. In addition, the proposed structure considerably filters out the off-axis input displacements of the PZT actuators and provides very small parasitic displacements at the output stage. Both channels exhibit almost identical dynamic responses in time and frequency domains, indicating highly symmetric fabrications of the nanopositioner and auxiliary parts for the installation of actuators and sensors.

This paper revisits a well studied leader-following consensus problem of linear multi-agent systems, while aiming at follower nodes' transient performance. Conventionally, when not all follower nodes have access to the leader's state information, distributed observers are designed to estimate the leader's state, and the observers are coupled via communication network. Then each follower node only needs to track its observer's state independently, without interacting with its neighbors. This paper deliberately introduces certain coupling effect among follower nodes, such that the follower nodes tend to converge to each other cooperatively on the way they converge to the leader. Moreover, by suitably designing the control law, the poles of follower nodes can be assigned as desired, and thus transient tracking performance can also be adjusted.

For a linear time varying (LTV) system containing stable and unstable modes, this article gives the necessary and sufficient conditions for asymptotic decoupling of stable modes. Establishment of the conditions relies on newly developed techniques for analyzing matrix exponential and state transition matrix. The research exploits fundamental properties of LTV systems and advances the knowledge base of linear control theory. The results can find a direct application in the autonomous synchronization problem for heterogeneous multiagent systems. The research methodology is based on rigorous theoretical proofs and numerical verification.

Cyber attacks can cause cascading failures and blackouts in smart grids. Therefore, it is highly necessary to identify the types, impacts and solutions of cyber attacks to ensure the secure operation of power systems. As a well-known practice, steady-state analysis is commonly used to identify cyber attacks and provide effective solutions. However, it cannot fully cover non-linear behaviours and cascaded blackouts of the system caused by dynamic perturbations, as well as provide a postdisturbance operating point. This study presents a novel approach based on dynamic analysis that excludes the limitations of the steady-state analysis and can be used in the events of various cyber attacks. Four types of common attacks are reviewed, and their dynamic impacts are shown on the IEEE benchmark model of the Western System Coordinating Council system implemented in MATLAB Simulink. Then, recommendations are provided to enhance the security of the future smart power grids from the possible cyber attacks.

A systematic stabilization approach is provided for systems whose regulation error dynamics is subject to rational nonlinearities given prior knowledge of the system zero-error steady-state condition and a proper internal model. The error dynamics is cast in a differential-algebraic form so as to address the synthesis of controller parameters by a numerical optimization problem subject to bilinear matrix inequality constraints. A particular case is also explored where the resulting constraints are linear matrix inequalities.

This paper proposes an encrypted observer-based control paradigm for enhancement of cybersecurity in networked control systems. The proposed paradigm exploits a semi-homomorphic encryption technique which enables the required computation to be done over encrypted data without any need for decryption at controller and observer levels. This improves the privacy of sensitive information such as command and sensor measurement signals. We study the challenges involved with the implementation of the proposed strategy and establish the conditions on system parameters to guarantee the stability of the closed-loop system. Some simulations experiments are performed on the Tennessee-Eastman process to illustrate the effectiveness of the proposed approach.

© 2015 IEEE. Collective control of a multi-Agent system is concerned with designing strategies for a group of autonomous agents operating in a networked environment. The aim is to achieve a global control objective through distributed sensing, communication, computing, and control. It has attracted many researchers from a wide range of disciplines, including the literature of automatic control. The present paper aims to give a general framework that is able to accommodate many of these outcomes. Within this framework, the development on this topic is systematically reviewed and the representative outcomes can be sorted out from four aspects: (i) agent dynamics, (ii) network topologies, (iii) feedback and communication mechanisms, and (iv) collective behaviors. Thus, the state-of-The-Art approach and technology is described. Moreover, within this framework, further interesting and promising directions on this research topic are envisioned.

© 1963-2012 IEEE.The paper aims to establish a general framework for robust output synchronization of a group of networked agents. The agents under investigation have nonlinear, uncertain and heterogeneous dynamics. Output synchronization denotes that all agents, through collaborative control, achieve output agreement and follow a desired pattern. In particular, the agreed trajectory is not defined by nor known to any agent in advance. Collaborative control is achieved using only output information from neighboring agents. Two concurrent actions are revealed in the proposed synchronization framework. This framework involves design strategies for both perturbed consensus and perturbed regulation problems, subject to a class of small gain conditions. The success of the framework is verified by constructive proof and numerical simulation.

In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with non-uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities apart from a small number of scalar parameters that appear nonlinearly. Furthermore, the linear matrix inequalities are theoretically verified to be solvable when the communication delay is sufficiently small. The effectiveness of the proposed control protocol is illustrated by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problemcan be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid,while an affine formation is stabilizable over a directed graph in the d-dimensional space if and only if the directed graph is (d + 1)-rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights.

Output synchronization of heterogeneous multi-agent systems has been one of the most interesting cooperative control problems. This paper first gives a brief survey of the research on the problem from which we see that the problem can be solved in a two-step manner with the aid of a properly designed local reference for each agent: (i) a controller is designed for each agent to achieve the trajectory regulation of the agent output to its associated reference; (ii) network collaboration is added to achieve consensus among references. In the presence of system uncertainties, the robust trajectory regulation problem in (i) can be solved by an internal model design. In this paper, we formulate a novel robust asymptotic model matching problem which is less conservative than trajectory regulation and can be solved by a static controller not relying on an internal model. Moreover, network collaboration is designed in (ii) within the so-called output communication setting such that consensus among references occurs concurrently with robust asymptotic model matching. As a result, output synchronization of heterogeneous multi-agent systems is achieved with a novel approach.

The paper studies the anti-torque-windup control and flexible vibration suppression problems on the coordinated positioning of the base attitude and manipulator joints of a free-floating flexible-joint dual-arm space robot. The full-actuated dynamic equations of flexible-joint dual-arm space robot with an attitude-controlled base are derived by using the linear momentum conservation and Lagrange method. With the flexibility compensating and singular perturbation technology, singular perturbation model of the system is obtained. To suppress the joint flexible vibration of two arms, a torque differential state feedback control strategy is presented for the fast subsystem. Meanwhile, an anti-torque-windup control method based on the torque active constraint design is proposed for the slow subsystem to track the desired positions of the base attitude and joints, and then the control saturation problems of the actual base attitude control system and joint motors are avoided. The obtained simulation results show that the proposed control scheme can accurately position the base attitude and two arms' joint, suppress the flexible vibration of joints and limit the output amplitude of the actual control torques effectively.

In machining process, chatter is an unstable dynamic phenomenon which causes overcut and quick tool wear, etc. To avoid chatter, traditional methods aim to optimize machining parameters. But they have inherent disadvantage in gaining highly efficient machining. Active magnetic bearing (AMB) is a promising technology for machining on account of low wear and friction, low maintenance cost, and long operating life. The control currents applied to AMBs allow not only to stabilize the supported spindle but also to actively suppress chatter in milling process. This paper, for the first time, studies an integrated control scheme for stability of milling process with a spindle supported by AMBs. First, to eliminate the vibration of an unloaded spindle rotor during acceleration/deceleration, we present an optimal controller with proper compensation for speed variation. Next, the controller is further enhanced by adding an adaptive algorithm based on Fourier series analysis to actively suppress chatter in milling process. Finally, numerical simulations show that the stability lobe diagram (SLD) boundary can be significantly expanded. Also, a practical issue of constraints on controller output is discussed.

In this paper, a new method for stability analysis of a single degree of freedom (SDOF) cutting system with sinusoidal spindle speed variation (SSSV) is proposed. Based on the approximately periodic property of the time delay in the turning process and the delay decomposition method, novel criteria of stability analysis for an SDOF cutting system are presented. Moreover, a state feedback controller is designed to stabilize the system and improve the steady-state response. Numerical simulation shows the effectiveness of the method.

Nonlinearly parameterized systems are commonly encountered in control of practical systems. However, the conventional adaptive estimation and control strategies, based on the essential assumption of linear parameterization, are incapable of dealing with this class of systems. This incapability in turn becomes a bottleneck for prevalent applications of adaptive control. In literature, there have been some attempts to break through this bottleneck by investigating the characteristics of nonlinearities. However, it is still open for an implementable strategy that is powerful for nonlinearly parameterized systems as the certainty equivalence principle for linearly parameterized systems. This paper aims to contribute an attempt to this open problem by proposing a novel adaptive control approach. On the one hand, the controller is conceptually simple, and it does not explicitly rely on the expression of system nonlinearities. On the other hand, the controller is able to achieve system stability and parameter convergence.

The most attractive trait of collective animal behavior is the emergence of highly ordered structures (Cavagna A., Giardina I. and Ginelli F., Phys. Rev. Lett., 110 (2013) 168107). It has been conjectured that the interaction mechanism in pigeon flock dynamics follows a hierarchical leader-follower influential network (Nagy M., Ákos Z., Biro D. and Vicsek T., Nature, 464 (2010) 890). In this paper, a new observation is reported that shows that pigeon flocks actually adopt a much simpler two-level interactive network composed of one leader and some followers. By statistically analyzing the same experimental dataset, we show that for a certain period of time a sole leader determines the motion of the flock while the remaining birds are all followers directly copying the leader's direction with specific time delays. This simple two-level despotic organization is expected to save both motional energy and communication cost, while retaining agility and robustness of the whole group. From an evolutionary perspective, our results suggest that a two-level organization of group flight may be more efficient than a multilevel topology for small pigeon flocks.

This paper established a closed-loop temperature control system for a spatially-separated atomic layer deposition (S-ALD) reactor using generalized predictive control (GPC) algorithm. The GPC-based closed-loop control system rapidly and precisely stabilized the reactor temperature in the presence of thermal field disturbances. Compared with the proportion-integration differentiation (PID) control commonly used for S-ALD, the closed-loop GPC system attenuated reaction temperature oscillations when producing two-element nano-scale thin films. Furthermore, the proposed GPC system demonstrated the superiority in multi-element nano-laminates depositing efficiency by reducing the settling time with a substrate moving between different reactors. Electrical and optical properties of films verified the feasibility of the proposed GPC system. Finally, experimental results presented that the microstructure of the deposited ALD nanometer thin film was improved with the developed GPC system, compared with the PID strategy.

To solve the joint movement control problem of a flexible-joint dual-arm space robot system with an uncontrolled base under the effects of external disturbances and unknown load parameters, a singular perturbation augmented robust adaptive PD composite control method was proposed. On the basis of the under-actuated robot dynamic sub-equations and joint motor dynamic sub-equations, a singular perturbation correction model of robot system was established by using the flexibility compensating singular perturbation technique. Then, a composite control integrating the fast varying state feedback control and the augmented robust adaptive PD slowly varying control were designed for the flexible-joint dual-arm space robot with unknown upper bound external disturbances and unknown load parameters. The simulation results confirm that the influences of the joint flexibility, unknown external disturbances and unknown load parameters can be eliminated effectively by the presented control method, and the desired joint movement of dual-arm space robot can be achieved accurately.

© 2013 IEEE. For a multiagent system in free space, the agents are required to generate sufficiently large cohesive force for network connectivity preservation and sufficiently large repulsive force for collision avoidance. This paper gives an energy function based approach for estimating the control force in a general setting. In particular, the force estimated for network connectivity preservation and collision avoidance is separated from the force for other collective behavior of the agents. Moreover, the estimation approach is applied in three typical collective control scenarios including swarming, flocking, and flocking without velocity measurement.

The mechanisms that underlie fascinating inter-individual interactions among animal groups have attracted increasing attention from biologists, physicists, and system scientists. There are two well-known types of interaction patterns: hierarchical and egalitarian. In the former type, individuals follow their leaders, whereas they follow their neighbors in the latter. Using high-resolution spatiotemporal data derived from the free flights of a flock of pigeons, we show that pigeon flocks actually adopt a mode that switches between the two aforementioned strategies. To determine its flight direction, each pigeon tends to follow the average of its neighbors while moving along a smooth trajectory, whereas it switches to follow its leaders when sudden turns or zigzags occur. By contrast, when deciding how fast to fly, each pigeon synthesizes the average velocity of its neighbors. This switching mechanism is promising for possible industrial applications in multi-robot system coordination, unmanned vehicle formation control, and other areas.

A fastest consensus problem of topology fixed networks has been formulated as an optimal linear iteration problem and efficiently solved in the literature. Considering a kind of predictive mechanism, we show that the consensus evolution can be further accelerated while physically maintaining the network topology. The underlying mechanism is that an effective prediction is able to induce a network with a virtually denser topology. With this topology, an even faster consensus is expected to occur. The result is motivated by the predictive mechanism widely existing in natural systems.

In this paper, we consider consensus of a group of heterogeneous agents with nonlinear dynamics in the presence of system uncertainties. It requires that all agent states reach an agreement which is governed by specified reference dynamics. However, the reference dynamics do not generate a specific reference trajectory for feedback regulation for any agent. For this purpose, the proposed controller integrates two fundamental actions, homogenization and consensus, concurrently. On one hand, it asymptotically regulates each individual (heterogeneous, nonlinear, and uncertain) agent dynamics to the common reference dynamics using a robust homogenization technique; on the other hand, it aligns agent trajectories, asymptotically governed by the common reference dynamics, to consensus through network cooperation. The effectiveness of the controller is verified in the rigorous proof and numerical simulation. © 2014 Elsevier B.V. All rights reserved.

The sliding-mode neural network control problem was discussed for a flexible-joint dual-arm space robot under the influences of parametric uncertainty and external disturbance. The elastic deformation of joint was described by the linear torsion spring, in terms of the principle of linear and angular momentum and the Lagrange method, the dynamic model of flexible-joint dual-arm space robot was derived. By using of the singular perturbation approach, two subsystems which can be controlled independently were separated from the system with the joint flexible compensation. To realize the accurately trajectory tracking of end-effectors on the effects of two uncertain factors and suppress the elastic vibration of joints, a hybrid control scheme composed by the sliding-mode neural network control of rigid motion and the feedback control of flexible motion was put forward. Simulation results show that the presented scheme has stronger ability to resist disturbance and parametric uncertainty, and can control the system to perform the desired circular motions and suppress the elastic vibration of joints.

Typical animal locomotion is achieved by the rhythmical undulation of its body segments while interacting with its environment. It inspires the mechanical design of multilink locomotors. With different postures, a multilink system may present different locomotion gaits. Recently, a so-called natural oscillation gait was studied for multilink systems, and a class of biologically inspired controllers was designed for the achievement of the gait. In this paper, the theoretical design is experimentally applied on a mechanical multilink testbed of two posture configurations in rayfish-like flapping-wing motion and snake-like serpentine motion. The effectiveness of the design is cross examined by theoretical analysis, numerical simulation, and experiments. © 2004-2012 IEEE.

We consider linear mechanical systems with asymmetric stiffness matrices. The class of systems captures essential body dynamics of animal/robotic locomotion. In particular, rhythmic body movements similar to those observed in animals can be found as a properly defined natural oscillation of the linear system. The objective is to design a nonlinear feedback controller that achieves the natural oscillation as a stable limit cycle for the closed-loop system. The controller structure we employ is inspired by neuronal circuits for animal locomotion. We translate the design requirement into a multivariable harmonic balance condition, and provide characterizations of neural controllers satisfying the condition. © 2013 Elsevier B.V. All rights reserved.

Collective circular motion is common in both natural systems and engineering applications. Recent theoretical research has intensively studied the fundamental control mechanism. This brief aims to pave the way from theoretical design to practical implementation by addressing a set of issues encountered in real applications. As a result, a practically effective control algorithm is successfully implemented and examined for a multirobot system to achieve a desired circular formation. © 1993-2012 IEEE.

The problems of joint motion control and flexible vibration suppression of a flexible joint space-based robot for manipulating an unknown payload are studied. Based on the system linear momentum conservation and the Lagrange method, the under-actuated dynamics model of the space robot is established. For convenience of the design of its control system, the system is divided into both fast and slow subsystems by using the joint flexibility compensation technique and the singular perturbation theory. A torque differential feedback controller is proposed for the fast subsystem to suppress the joints' flexible vibration, meanwhile an adaptive control scheme based on the augmentation approach is designed for the slow subsystem to realize the joint trajectory asymptotic tracking under the condition of unknown payload parameters. Because of introduction of the flexibility compensation technique, the presented control scheme can equivalently increase the joint stiffness, and it is suitable to control the space robot systems with low joint stiffness. Moreover, the effect of unknown parameters is real-time compensated by its adaptive controller, and then the specified joint motion task is achieved precisely. The effectiveness of the scheme is verified by the corresponding simulation results.

The design problem of a joint motion controller for a flexible-joint space robot with an uncontrolled base is discussed. With the linear and angular momentum conservation of the system and a Lagrangian method, the dynamic model of a space robot is established. To realize the control target of joint motion, an adaptive backstepping control scheme for a flexible-joint space robot is proposed via the function approximation technique of neural network. The presented control scheme need not know the information of system parameters, and avoids the measurements and feedback of the position-related variables of the base. Thusly, it is more suitable for practical applications. Numerical simulation results show that the control scheme proposed can obtain the smaller vibration of flexible joints and effectively control the space robot system to accomplish the desired joint motion.

The coordinated motion control and flexible vibration suppression problems of flexible space manipulator are studied. With the assumed mode method and the linear momentum conservation of the system, the system dynamics model of the space manipulator is derived. Based on the hybrid sliding mode concept, an adaptive variable structure control scheme is proposed for the flexible space manipulator to achieve the coordinated motion between the base's attitude and the arm's joints, which accounts for the uncertainty in inertial parameters. The hybrid sliding mode introduced consists of two parts, the frequency shaped optimal sliding mode and the terminal sliding mode. The former is used to suppress the vibration of flexible link of the system, and the latter is utilized to guarantee the convergence of system tracking errors in finite time. Moreover, the control scheme proposed does not require the foreknowledge of flexible variables in control. Thus, it can effectively avoid the real-time measurements and feedbacks of system flexible variables, and be more suitable for practical applications. Simulation results demonstrate the effectiveness of the proposed control scheme.

The robust control problem of a free-floating flexible-joint space robot with an uncontrolled base to track the desired trajectory in workspace is discussed. With the system linear and angular momentum conservation and Lagrangian method, the dynamic equations are derived. In the consideration of the strong joint flexibility of a space robot, a joint flexibility compensation controller is designed to compensate the effects of the joint flexibility to the system control precision. Then by using of the singular perturbation technology, a robust control scheme for the robot system with uncertain inertial parameters to track the desired trajectory in workspace is presented. A planar space robot system with flexible joints is simulated to verify the effectiveness of the proposed control method.

The dynamic modeling and singular perturbation control problems of free-floating space robot with normal flexible joints and an uncontrolled base were discussed. With the relationship of the system linear and angular momentum conservation, a system dynamics model was established by Lagrangian formulation. To eliminate the limitation of joint flexibility for applications of the traditional singular perturbation control technique in space robot with normal flexible joints, a joint flexibility compensator was introduced, which can level down the equivalent joint flexibility of the system. And then with the help of singular perturbation theory, the singular perturbation control schemes for free-floating space robot with flexible joints to track the desired trajectory in joint space and inertial space were designed successively. The control schemes presented are more suitable for the control of space robot systems with normal flexible joints, because of no joint flexibility limitation. Theoretical analysis and simulation results verify the feasibility of the proposed control schemes.

The compensation control problems of space-based robot system with external disturbances were studied. The dynamic equations of the system were given firstly. Then, with the augmentation approach, the augmented adaptive neural network compensation control schemes were developed for space-based robot with unknown inertial parameters and external disturbances to track the desired trajectories in joint space and in inertial space, respectively. The control schemes proposed don't require the measurements and feedback of the position, linear velocity and acceleration of the base. Besides, compared with traditional adaptive control schemes, they can avoid linearly parameterizing the dynamic equations of the system and subsequently reduce tedious computations during the determination of the regression matrix for the system. The simulation results validate the presented control schemes.

The control problem of free-floating space robot system with dual-arm is studied. The dynamic equations of the system are formulated by the under-actuated form to guarantee that they can be linearly parameterized. With the augmentation approach, the dynamics of the system is analyzed and the augmented generalized Jacobi matrix of the system can also be linearly dependent on a group of inertial parameters. Based on the results, a robust-adaptive combined control scheme is developed for dual-arm space robot system with external disturbances and uncertain payload parameters to track the desired trajectories in inertial space. Comparing with the adaptive control, the control scheme proposed can effectively reduce the calculation time, because it can transfer many integral operations into four arithmetic operations. Therefore, it is suitable for real-time and on-line applications in space-based robot system. The simulation results verify the proposed control scheme.

The compensation control problems of coordinated motion between the base's attitude and two end-effector of a free-floating dual-arm space robot with unknown external disturbances to track the desired trajectories were discussed. With the linear momentum conservation of the system, the kinematics and dynamics of the system were analyzed, and then the dynamics equations of the system described in workspace were derived. Based on the results, a neural network on-line self-learning compensation control scheme for coordinated motion of the free-floating dual-arm space robot with unknown external disturbances was designed. The control scheme proposed can avoid the measurements of the position-related variables of the base, and effectively enhance the robustness and adaptive ability of the system because of the good on-line self-learning compensation of the neural network for external disturbances. Simulation results validate the feasibility of the presented control scheme.

A scheme of fuzzy terminal sliding mode control was proposed for vibration suppression of a flexible space manipulator base position of which was not controlled. The dynamical equation of the flexible space manipulator was derived by using the assumed mode method, linear momentum conservation of the system and the Lagrange method. To solve the problems of trajectory tracking control and vibration suppression of the flexible space manipulator, the singular perturbation approach was adopted to decompose the manipulator system into a slow subsystem and a fast subsystem. And then, the controller could be designed separately for the subsystems. A fuzzy terminal sliding mode control scheme was designed to control the slow subsystem and the linear quadratic regulator (LQR) based on the reduced order observer was proposed for the fast subsystem. A simulation example of flexible space manipulator demonstrates that the control scheme not only guarantees that the tracking errors of the base's attitudes and arm's joints of the system converge to zero in finite time, but also weakens the chattering of the sliding mode controller and the vibration of the flexible arm effectively.

The objective of the present work is to predict compressible swirl flow in the nozzle of air-jet spinning using the realizable k-e turbulence model and discuss the effect of the nozzle pressure. The periodic change of flow patterns can be observed. The recirculation zone near the wall of the injectors upstream increases in size and moves gradually upstream, whereas the vortex breakdown in the injector downstream shifts slowly towards the nozzle outlet during the whole period. A low axial velocity in the core region moves gradually away from the centerline, and the magnitude of the center reverse flow and the area occupied by it increase with axial distance due to the vortex breakdown. From the tangential velocity profile, there is a very small free-vortex zone. With increasing nozzle pressure, the velocity increases and the location of vortex breakdown is moved slightly downward. However, the increase in the velocity tends to decline at nozzle pressure up to a high level. Copyright © 2008 John Wiley & Sons, Ltd.

The research on biofacies and its provincialization is of important significance not only for the increasing of precision of stratigraphic subdivision and correlation in South China, the reconstruction of ancient environment and paleogeography and even the guiding of oil and gas exploration, but also for the study of paleobiogeogrphy and sea level changes of southern China in Ordovician. On the basis of the studies of the ecological characteristics of Ordovician cephalopods from South China, eighteen cephalopod biofacies are recognized and described: (1) Open platform Proterocameroceras biofacies; (2) Restricted platform Pseudoectenolites-Xiadongoceras biofacies; (3) Open platform Retroclitendoceras-Pararetroclitendoceras biofacies; (4) Open platform Pronajaceras-Mamagouceras biofacies; (5) Shelf slope-basin Cyclostomiceras biofacies; (6) Open platform Cameroceras-Cyrtovaginoceras biofacies; (7) Open platform Coreanoceras-Manchuroceras biofacies; (8) Shelf slope-basin Kaipingoceras-Kyminoceras biofacies; (9) Inner shelf Bathmoceras-Protocycloceras biofacies; (10) Middle shelf Dideroceras-Ancistroceras biofacies; (11) Deep-water shelf Lituites-Cyclolituites biofacies; (12) Stagnant basin Lituitet-Trilacinoceras biofacies; (13) Deep-water basin Paraendoceras-Sactorthoceras biofacies; (14) Deep-water shelf Sinoceras-Michelinoceras-Disoceras biofacies; (15) Deep-water shelf Beloitoceras-Jiangshanoceras biofacies; (16) Deep-water shelf-basin Eurasiaticoceras biofacies; (17) Shelf-slope Jiangxiceras-Yushanoceras biofacies; (18) Deep-water basin Michelinoceras biofacies. The cephalopods of these biofacies, their ecological characteristics, and living conditions are elucidated in this article. The association law of cephalopod biofacies in time and space shows that there were three cephalopod biofacies provinces in South China during the Ordovician, i. e., Yangtze biofacies province, East Guizhou ({A figure is presented})-West Hunan ({A figure is presented}) biofacies province (mixed-type biofacies province), and Central Hunan-West Zhejiang ({A figure is presented}) biofacies province. It is suggested that differentiation of cephalopod biofacies was mainly controlled by sea level changes and tectonic evolution. The differentiation is obvious during lower sea level and not developed during high sea level. © 2006 China University of Geosciences.

The global robust output regulation problem for the class of nonlinear systems in output feedback form has been studied under the assumption that the solution of the regulator equations is polynomial. This assumption essentially requires these systems contain only polynomial nonlinearity and is due to the failure of finding a nonlinear internal model to account for more complex nonlinearities than polynomials. Recently, it was found that a nonlinear internal model can be constructed under some assumption much milder than the polynomial assumption. In this note, we will apply this type of internal model to solve the global robust output regulation problem for the class of nonlinear systems in output feedback form. © 2005 IEEE.

Uniform-sized molecularly imprinted polymer (MIP) beads were prepared using a one-step swelling and polymerization method. The obtained sulfamethazine (SMZ)-imprinted polymer showed high affinity and selectivity toward SMZ and other structurally related sulfonamides in acetonitrile or water-acetonitrile mobile phases, particularly in high aqueous systems. The column performance of the MIPs for SMZ and its analogues could be improved by elevating the column temperature and optimizing the flow rate. The hydrogen-bonding effect plays a significant role in the recognition process of SMZ-imprinted polymer systems in organic media, while the ion-exchange effect, as well as hydrophobic effect, dominantes the retention mechanism in aqueous-rich media, in addition to shape recognition. Copyright © 2005 John Wiley & Sons, Ltd.

For over a decade, the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neutrally stable. Thus, the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions. In this paper, we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems. An example with the well known van der Pol oscillator as the exosystem is given to illustrate our approach. © 2005 Elsevier Ltd. All rights reserved.

While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neutrally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then, we give conditions under which the problem can be solved by solving a robust stabilization problem of an augmented system. Finally, we apply our general result to obtain the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems. © 2005 IEEE.

Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. In this paper, we establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability. © 2004 IEEE.

This paper presents a technical framework utilizing the dissipativity mechanism that gives rise to the solution of the global regulation problem of the cascade-connected systems subject to both dynamic uncertainty and static uncertainty without knowing the bound of the static uncertainty. Additionally, this paper shows that the nonlinear robust servomechanism problem for the lower triangular systems can be cast into the regulation problem for the cascade-connected systems, thus leading to a complete solution of the nonlinear robust servomechanism problem for the lower triangular systems for the most general case where both the uncertain parameters and the exogenous signals can be arbitrarily large.

The global robust servomechanism problem (alternatively, global robust output regulation problem) for lower triangular systems has been studied for two special cases. The first case assumes that the systems only contain polynomial nonlinearities, and the second case limits the exogenous signals and the unknown parameters to be within a known bounded set. This paper presents the solvability conditions of the global robust servomechanism problem for the lower triangular systems for the most general case where neither of the above two assumptions is needed. Our approach consists of two steps. In the first step, we convert the problem into a global adaptive regulation problem for lower triangular systems subject to both dynamic and static uncertainties. In the second step, we derive the solvability conditions of the problem by appealing to the recent result on the solvability of the global adaptive regulation problem for lower triangular systems with both dynamic and static uncertainties. © 2003 Elsevier B.V. All rights reserved.

The output regulation problem of singular nonlinear systems via the normal output feedback control has been a challenging problem. Existing approaches for solving this problem employed techniques similar to those used for linear singular systems. Results from these approaches either rely on a normalizability assumption or are limited to systems with special structures. This note gives a complete solution for this problem by employing a novel approach that is also interesting for linear systems.

Global robust stabilization of nonlinear cascaded systems is a challenging problem when the zero-dynamics is not exponentially stable. Recently, some recursive procedure has been developed for handling this problem utilizing the small gain theorem. However, the success of the procedure depends on the satisfaction of some conditions which arise at each step of the recursion. In this paper, we will show that, for the important class of cascaded polynomial systems, the solvability conditions can be made satisfied by appropriately implementing the recursive procedure. This result leads to an explicit construction of the control law. © 2002 Elsevier Science B.V. All rights reserved.