Passivity‐based state synchronization of homogeneous multiagent systems via static protocol in the presence of input saturation

This paper studies semiglobal and global state synchronization of homogeneous multiagent systems with partial‐state coupling (ie, agents are coupled through part of their states) via a static protocol. We consider 2 classes of agents, ie, G‐passive and G‐passifiable via input feedforward, which are subjected to input saturation. The proposed static protocol is purely decentralized, ie, without an additional channel for the exchange of controller states. For semiglobal synchronization, a static protocol is designed for an a priori given set of network graphs with a directed spanning tree. In other words, the static protocol only needs rough information on the network graph, ie, a lower bound for the real part and an upper bound for the modulus, of the nonzero eigenvalues of the corresponding Laplacian matrix. Whereas for global synchronization, only strongly connected and detailed balanced network graphs are considered. In this case, for G‐passive agents, the static protocol does not need any network information, whereas for G‐passifiable agents via input feedforward, the static protocol only needs an upper bound for the modulus of the eigenvalues of the corresponding Laplacian matrix.     

Regulated state synchronization of homogeneous multiagent systems with partial‐state coupling via low‐gain adaptive protocol

This paper studies regulated state synchronization for continuous‐time homogeneous multiagent systems with weakly unstable agents where the reference trajectory is given by a so‐called exosystem. The agents share part of their state over a communication network. We assume that the communication topology is completely unknown and directed. An algebraic Riccati equation–based low‐gain adaptive nonlinear dynamic protocol design is presented to achieve the regulated state synchronizations. Utilizing the adaptive control, our nonlinear dynamic protocol is universal and does not depend on any information about the communication topology or the number of agents.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Fixed‐time state estimation for a class of switched nonlinear time‐varying systems

This paper deals with the state estimation problem of a class of nonlinear time‐varying systems with switched dynamics. Based on the concept of fixed‐time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time‐varying systems with state jumps, satisfying the minimal dwell‐time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.     

Sampled‐data consensus of multiagent systems with switching jointly connected topologies via time‐varying Lyapunov function approach

Consensus problem of multiagent systems with switching jointly connected topologies under sampled‐data control is studied in this article. The main contribution is that the consensus problem for such system is solved without the assumption that the system matrices are stable or critically stable. For this purpose, a time‐varying Lyapunov function method is utilized to describe the state characteristics with switching jointly connected topologies. Based on the time‐varying matrix of Lyapunov function, the “decline” characteristics at the switching instants is derived to compensate the divergence among the agents with disconnected topologies. Utilizing the “decline” characteristics, the overall consensus of such system can be guaranteed in the framework of dwell time. Finally, the effectiveness of the proposed result is illustrated by two numerical examples.     

Consensus of multiagent systems with nonlinear dynamics and time‐varying communication delays

This paper deals with the local consensus of multiagent systems with nonlinear dynamics communication delays simultaneously. By introducing a weighted average state and applying the properties of the Laplacian matrix eigenvalues, the system is decoupled into several subsystems, firstly, to reduce complexity of theory analysis. Then, a new augmented vector containing single and double integral terms is constructed and the corresponding Lyapunov functional with triple integral terms is introduced. Meanwhile, in order to improve the estimating accuracy of the derivatives of constructed Lyapunov functional, single integral inequalities and double integral inequalities via auxiliary functions, an extended relaxed integral inequality and an reciprocally convex approach are used, as a result, stability criterion with less conservatism is derived, which guarantees the local consensus of the considered systems. Finally, numerical examples are provided to check the improvement of the proposed method over the existing works.     

H2 and H∞ almost output synchronization of heterogeneous continuous‐time multi‐agent systems with passive agents and partial‐state coupling via static protocol

This paper studies H₂ and H_∞ almost output synchronization problems for heterogeneous continuous‐time multiagent systems with passive agents and strongly connected communication graph. For non‐introspective passive agents, a linear static protocol can be designed to achieve almost output synchronization with arbitrarily small H₂ norm. Moreover, we show that the H_∞ almost output synchronization problem via static protocol is not solvable for this class of systems.     

On time‐varying formation feasibility and reference function of time‐delayed linear multiagent systems with switching digraphs

Time‐varying formation feasibility and formation reference function of linear multiagent systems with both time‐varying delays and switching directed topologies are studied. For a given linear multiagent system, not all the time‐varying formations can be realized due to the dynamic restriction of each agent. The formation feasibility constraint reveals the requirement on the desired time‐varying formation to be compatible with the agent dynamics. Formation reference is a representation for the macroscopic movement of the whole multiagent system. Novel features of the formation feasibility constraint and the formation reference are the main focus of this paper. Firstly, a time‐delayed formation control protocol with switching directed topologies is constructed using local neighboring information. Then, a time‐varying formation feasibility constraint is derived based on nonsingular transformations. It is proven that the time‐varying formation feasibility constraint is independent of the time‐varying delays and the switching directed topologies. Moreover, an explicit expression of the formation reference function is proposed. It is shown that neither the time‐varying delays nor the switching directed topologies has influence on the obtained formation reference function. Finally, comparative examples are provided to demonstrate the obtained results.     

Reduced‐order state estimation for linear time‐varying systems

We consider reduced‐order and subspace state estimators for linear discrete‐time systems with possibly time‐varying dynamics. The reduced‐order and subspace estimators are obtained using a finite‐horizon minimization approach, and thus do not require the solution of algebraic Lyapunov or Riccati equations. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust time‐varying formation design for multiagent systems with disturbances: Extended‐state‐observer method

Robust time‐varying formation design problems for second‐order multiagent systems subjected to external disturbances are investigated. First, by constructing an extended state observer, the disturbance compensation is estimated, which is a critical term in the proposed robust time‐varying formation control protocol. Then, an explicit expression of the formation center function is determined and impacts of disturbance compensations on the formation center function are presented. With the formation feasibility conditions, robust time‐varying formation design criteria are derived to determine the gain matrix of the formation control protocol by utilizing the algebraic Riccati equation technique. Furthermore, the tracking performance and the robustness property of multiagent systems are analyzed. Finally, the numerical simulation is provided to illustrate the effectiveness of theoretical results.     

Finite‐time stability of switched nonlinear time‐varying systems via indefinite Lyapunov functions

This note considers the problem of finite‐time stability (FTS) for switched nonlinear time‐varying systems. First, a relaxed condition is proposed to verify the FTS of nonlinear time‐varying systems by using an indefinite Lyapunov function. Then, the result obtained is extended to study the FTS of switched nonlinear time‐varying systems. Several relaxed conditions are given by using a common indefinite Lyapunov function and multiple indefinite Lyapunov functions. Moreover, the corresponding estimates on convergence regions and times of systems are also given. Comparing with the existing results, the conditions obtained allow the time derivative of Lyapunov functions of subsystems (or systems) to be indefinite and all subsystems to be not finite‐time stable or even unstable. Finally, a numerical example is given to illustrate the theoretical results.     

Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects

This paper considers the input‐to‐state stability, integral‐ISS, and stochastic‐ISS for impulsive nonlinear stochastic systems. The Lyapunov function considered in this paper is indefinite, that is, the rate coefficient of the Lyapunov function is time‐varying, which can be positive or negative along time evolution. Lyapunov‐based sufficient conditions are established for ensuring ISS of impulsive nonlinear stochastic systems. Three examples involving one from networked control systems are provided to illustrate the effectiveness of theoretical results obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Controllability of discrete‐time multiagent systems with switching topology

The current theoretical investigation on the controllability of switched multiagent systems mainly focuses on fixed connected topology or union graph without nonaccessible nodes. However, for discrete‐time multiagent systems with switching topology, it is still unknown whether the existing results are valid or not under the condition of arbitrary topology. Based on graph distance partitions and Wonham's geometric approach, we provide the lower and upper bounds for the dimension of controllable subspaces of discrete‐time multiagent systems. Unlike the existing results of controllability with switching topology, the proposed results have the advantage of being applicable to multiagent systems with arbitrary graphic topologies, union graph (strongly connected or not), and coupling weights. We also provide 2 algorithms for computing the lower and upper bounds for the dimension of controllable subspaces, respectively. Furthermore, as a remarkable application, we present how the proposed lower bound can be utilized for achieving the targeted controllability if the dimension of the controllable subspace of the switched system satisfies certain conditions.     

Scaled consensus for asynchronous high‐order discrete‐time multiagent systems

This paper investigates the distributed scaled consensus problem of multiple agents with high‐order dynamics under the asynchronous setting, where each agent measures the neighbors' information at certain discrete time instants according to its own clock rather than the whole discrete process and all agents' clocks are independent of each other. Assume that the communication topology can be arbitrarily switched and the information transfer between agents has a time‐varying delay. Under the designed asynchronous distributed control protocol, it is shown that the agents with the same scale will reach a common final state, while the agents with different scales will reach different final states. Moreover, an effective parameters selection strategy is presented for a large number of gain parameters in high‐order multiagent systems based on novel model transformation techniques. Simulation examples are provided to demonstrate the high‐order scaled consensus performances for the agents in the presence of asynchronous setting.     

Compensation of time‐varying input delay for discrete‐time nonlinear systems

We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.     

IQC‐based robustness analysis of discrete‐time linear time‐varying systems

The paper investigates the robust stability and performance of uncertain linear time‐varying (LTV) systems using an integral quadratic constraint (IQC) based analysis approach. Specifically, previous theoretical work on IQC‐based robustness analysis of linear time‐invariant (LTI) systems is extended to discrete‐time LTV systems. In the case of a general LTV nominal system, the analysis solution is provided in terms of an infinite‐dimensional convex optimization problem. This optimization problem reduces into a finite‐dimensional semidefinite program when the nominal system in question is finite horizon, periodic, or, more generally, eventually periodic. Finally, the results are applied to an unmanned aircraft control system executing an aggressive maneuver, where the developed techniques are used to find the region in which the aircraft is guaranteed to reside at the end of its planned trajectory. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed integral‐type event‐triggered synchronization of multiagent systems

This paper investigates the synchronization problem of generic linear multiagent systems via integral‐type event‐triggered control. Each agent can only utilize the intermittent information of its neighboring agents in the control scheme. Based on the integral‐type event conditions, an event‐triggered control protocol is designed to guarantee the synchronization of multiagent systems, and Zeno behavior is excluded by showing the existence of a positive lower bound on the inter‐event intervals. Then, we propose the integral‐type event‐triggered control algorithms to study the leader‐following synchronization. It is shown that under the control algorithms all the followers track the leader and no Zeno behavior occurs. The effectiveness of the proposed control schemes is demonstrated by simulation examples.     

Krasovskii and Razumikhin criteria on input‐to‐state stability of discrete‐time time‐varying switched delayed systems

In this article, we are concerned with the problem on input‐to‐state stability (ISS) for discrete‐time time‐varying switched delayed systems. Some Krasovskii and Razumikhin ISS criteria are provided by using the notions of uniformly asymptotically stable (UAS) function and mode‐dependent average dwell time (MDADT). With the help of the concept of UAS function, the advantage of our results in this article is that the coefficients of the first‐order difference inequalities for the mode‐dependent Krasovskii functionals and mode‐dependent Razumikhin functions are allowed to be time‐varying, mode‐dependent, and can even take both positive and negative values, and the whole switched system can be allowed to have both ISS subsystems and non‐ISS subsystems. With the aid of the notion of MDADT, each subsystem can have its own average dwell time. As an application, we also provide an ISS criterion for discrete‐time time‐varying switched delayed Hopfield neural networks with disturbance inputs. Numerical simulations verify the effectiveness of the established criteria.