Intermittent observer-based consensus control for multi-agent systems with switching topologies

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach.     

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

In this paper, the consensus tracking problem with unknown dynamics in the leader for the linear multi-agent systems is addressed. Based on the relative output information among the agents, decentralised adaptive consensus protocols with static coupling gains are designed to guarantee that the consensus tracking errors converge to a small neighbourhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded. Moreover, the result is extended to the case with dynamic coupling gains which are independent of the eigenvalues of the Laplacian matrix. Both of the protocols with static and dynamic coupling gains are designed by using the relative outputs, which are more practical than the state-feedback ones. Finally, the theoretical results are verified through an example.     

多智能体网络系统的自适应协调控制

为实现多智能体网络系统的协调控制,设计了一种新型的带有自适应协调器的控制器.基于动态图建立了多智能体网络系统的模型,并考虑了系统的非线性互联和不可避免存在的时变时滞.应用分布式控制策略,设计了自适应参数估计的协调器,用于调节智能体之间的互联强度,使网络达到稳定的预设水平.并基于Lyapunov-Kra-sovskii泛函和自适应动态偏差反馈控制技术,根据拉萨尔不变集原理证明了偏差控制系统的渐近收敛性.这种控制方法,可在系统参数不确定的情况下,同时完成参数估计和协调控制.所设计的控制律和自适应律简单,易于实现,仿真示例验证了所提方法的有效性.     

Adaptive neural network tracking design for a class of uncertain nonlinear discrete-time systems with dead-zone

In this paper, the stability and control issues of a class of uncertain nonlinear discrete-time systems in the strict feedback form are investigated. The dead-zone input in the systems, whose property is non-symmetric and discretized, is investigated. The unknown functions in the systems are approximated by using the radial basis function neural networks （RBFNNs）. Backstepping design procedure is employed in the controller and the adaptation laws design. Lyapunov analysis method is utilized to prove the stability of the closed-loop system. A simulation example is given to illustrate the effectiveness of the proposed approach.     

Adaptive quantized control for linear uncertain discrete-time systems

A direct adaptive control framework for linear uncertain systems for using communication channels is developed. Specifically, the control signals are to be quantized and sent over a communication channel to the actuator. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability, that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. The quantizers are logarithmic and characterized by sector-bound conditions, with the conic sectors adjusted at each time instant by the adaptive controller, in conjunction with the system response. Furthermore, we extend the scheme to the case where the logarithmic quantizer has a deadzone around the origin so that only a finite number of quantization levels is required to achieve practical stability. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.     

Controllability of multi-agent systems with periodically switching topologies and switching leaders

This paper considers controllability of multi-agent systems with periodically switching topologies and switching leaders. The concept of m-periodic controllability is proposed, and a criterion for m-periodic controllability is established. The effect of the duration of subsystems on controllability is analysed by utilising a property of analytic functions. In addition, the influence of switching periods on controllability is investigated, and an algorithm is proposed to search for the fewest periods to ensure controllability. A necessary condition for m-periodic controllability is obtained from the perspective of eigenvectors of the subsystems’ Laplacian matrices. For a system with switching leaders, it is proved that switching-leader controllability is equivalent to multiple-leader controllability. Furthermore, both the switching order and the tenure of agents being leaders have no effect on the controllability. Some examples are provided to illustrate the theoretical results.     

Properties of linear switching time-varying discrete-time systems with applications

We study two discrete-time, linear switching time-varying (LSTV) structures, each of which consists of a periodic switch connected to several linear time-invariant (LTI) systems. Such structures can be used to represent any linear periodically time-varying (LPTV) systems. We give basic properties associated with the LSTV structures in terms of their LTI building blocks, and then apply the results to solve a general approximation problem: How to optimally approximate an LPTV system with period p by an LPTV system with period ? The optimality is measured using norms. The study is extended to general multirate periodic systems.     

Stability analysis for planar discrete-time linear switching systems via bounding joint spectral radius

A pair of 2-by-2 matrices can be transformed into the joint forms, which are bound together via an invariant that measures the deformation of their structures with respect to each other. With this, we obtain an approximation of the joint spectral radius of such a pair of matrices from above and then apply it to assessing stability for planar discrete-time linear switching systems.     

Robust cooperative output tracking of networked high-order power integrators systems

This paper focuses on a robust cooperative output tracking problem of networked power integrator systems. The dynamics of each system is considered as a nonlinear high-order power integrator whose linearised model is uncontrollable around its origin. It is proven via Lyapunov Theory that under some mild assumptions and graph structural properties, all agents’ outputs in the network can be synchronised to a desired trajectory with a bounded error in the presence of external disturbances as well as model uncertainties. Moreover, the tracking performance can be tuned by appropriately choosing parameters within the controller. The proposed controller for each agent is in the essence constructed via backstepping technique consisting of three components: the state feedback of its own, the outputs of its neighbours and the information of the desired trajectory if connected, and thus in a distributed manner.     

Robust control of linear discrete-time systems

Given a linear discrete-time system with additive disturbances, a general methodology for designing a stable control algorithm is shown. The approach is Lyapunov-based with certain liberty of tailoring the candidate function for a given problem. Comparison to the existing solutions based on a variable structure approach is given.     

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.     

Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ?₂-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel

The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed.     

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.     

Observer-based optimal output tracking for discrete-time systems with multiple state and input delays

The optimal output tracking control (OOTC) problem for a class of discrete-time systems with state and input delays is addressed. An augmented system is constructed such that the OOTC problem can be transformed into a two-point boundary value (TPBV) problem with both advance and delay terms from the necessary optimality conditions. The successive approximating method recently developed is extended to obtain an approximate solution of the TPBV problem, which is then used to obtain a feedforward and feedback tracking controller. An observer is designed for the uncertain reference input such that the feedforward controller is physically realizable. Simulations show the results are effective even with long time-delays. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il Lee. This research was supported by the National Natural Science Foundation of China (Grant No. 40776051), the Key Natural Science Foundation of Shandong Province (Grant No. Z2005G01), the Natural Science Foundation of Qingdao City (Grant No. 05-1-JC-94) and the research funds of QingDao University of Science and Technology. Hai-Hong Wang received the Ph.D. degree in Computer Science in July 2007 from Ocean University of China. She presently works in QingDao University of Science and Technology, Qingdao, P.R. China. Her current research interests include analysis and control for time-delay systems and nonlinear systems. Gong-You Tang received the Ph.D. degree in Control Theory and Applications from the South China University of Technology, P. R. China in 1991. He is a Professor at the College of Information Science and Engineering at the Ocean University of China, Qingdao, P. R. China. He is the Editor of the Journal of the Ocean University of China and Control and the Instruments in Chemical Industry. His research interests are in the areas of nonlinear systems, delay systems, large-scale systems, and networked control systems, with emphasis in optimal control, robust control, fault diagnosis and stability analysis.     

Adaptive output feedback tracking control for a class of uncertain switched nonlinear systems under arbitrary switching

This paper investigates the problem of adaptive output feedback tracking for uncertain switched nonlinear systems, under arbitrary switching. First, an adaptive output feedback controller is designed, which ensures the boundedness of all the closed-loop signals. Then, a novel adaptive-based robust output feedback control is proposed to drive the tracking error to zero, in which the bound of disturbances is not required to be known in advance. Both control algorithms are based on the common Lyapunov function method, without any restrictions on dwell time. To evaluate the performance of the proposed output feedback control schemes, a numerical example is presented and discussed.     

Consensus tracking for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state

In this study, the authors consider the consensus tracking problem for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state. The dynamics of each agent consists of nonlinear inherent dynamics. In order to reach consensus tracking, a class of nonsmooth control protocols is proposed which only depends on the agent's own information and its neighbours’ information. With the aid of algebraic graph theory, matrix theory, and Lyapunov theory, some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived. Finally, the numerical simulations are given to illustrate the effectiveness of the developed theoretical results.