Consensus of switched multi-agents system with cooperative and competitive relationship

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

Robust consensus for linear multi-agent systems with mixed uncertainties

In this paper, we study the cooperative output regulation problem for a class of second-order linear uncertain multi-agent systems with unknown exosystem. We first present a distributed canonical internal model to convert the cooperative output regulation problem for the original plant into a stabilization problem for its augmented system. Then we solve the problem via a distributed state feedback controller by combining the distributed internal model approach and the adaptive control technique. Our design is illustrated by an example.

In this article, a leader-follower asymptotic consensus control strategy is developed for a class of linear multiagent systems (MASs) with unknown external disturbances and measurement noises. First, the preconditions, the minimum phase condition (MPC) and observer matching condition (OMC), are discussed in detail, and an equivalent result under these two preconditions is given. In this way, the corresponding results from Corless and Tu (1998) are improved. Meanwhile, a reduced-order observer is designed for a constructed augmented system to estimate the system states and noises of each agent. Next, with the help of a traditional interval observer, a novel unknown disturbance reconstruction method is developed, and the reconstruction can converge to the unknown disturbance asymptotically and decouple from the control input. The subsequent asymptotic consensus is accomplished by utilizing an observer-based control scheme, with its design satisfying the so-called separation principle. Finally, two simulation examples are given to verify the effectiveness and show the advantages of the proposed methods.

This brief studies the time-varying formation (TVF) control of linear multi-agent systems (MASs), where the communication topology switches from several different topologies and the switching signal is depicted by a right-continuous Markov process. The communication noises are taken into account simultaneously, which are described as independent white noises with noisy intensities. A class of stochastic-approximation type control protocols is given and certain sufficient conditions are derived for realizing the TVF stabilization in mean square sense. Moreover, the indicative function and infinitesimal generator are imported in Lyapunov functions to help proving that the MASs can be formed into stable TVF shapes with the proposed control protocols. In the end, an simulation example is performed to state the availability of the approach.

This paper addresses the event-triggered consensus tracking for general linear multi-agent systems with nonlinear uncertainty dynamics under directed communication topology. The proposed event-triggered consensus strategy relaxes the assumptions in existing works that the control gain and local inputs must be continuous. With the consensus tracking condition being satisfied, the cooperative control law with bounded parameter is developed based on the intermittent samples. It shows that if the sampling condition, in terms of LMIs, is satisfied, the resulting closed-loop general linear multi-agent uncertain systems will achieve the consensus. Simulation results are provided to verify the proposed approach.

In this paper, the problem of the robust unknown input observer for a class of linear multi-agent systems and its application to fault estimation are considered. First, an undirected graph is used to represent the communication topology of a leader---follower linear multi-agent system. Then, using relative output estimation errors among agents, an unknown input observer is proposed to achieve fault estimation for the global augmented system in which the actuator or sensor fault vector is taken as an auxiliary state vector. A multi-constrained design algorithm based on linear matrix inequality technique is also designed to obtain gain matrices of unknown input observer. Simulation results show the effectiveness and advantages of the proposed robust unknown input observer method for fault estimation of multi-agent systems.

The cooperative output regulation of a linear multi-agent system can be viewed as a generalization of the leader-following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi-agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi-agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi-agent system. We then solve our problem by combining a simultaneous high-gain state feedback control technique and a distributed high-gain observer technique. A special case of our result leads to the solution of the leader-following robust consensus problem for a class of uncertain multi-agent systems. Copyright © 2013 John Wiley & Sons, Ltd.

This paper studies a class of discrete-time impulsive switched delayed systems with delay-dependent impulses, aiming to solving the input-to-state stability (ISS) problem in the case of asynchronous switching signal between subsystem and controller and asynchrony of switching signals and impulsive signals. Among them, the delay effect is handled by a new Lyapunov-Krasovskii function divided into a delay-dependent part and a delay-independent part. In contrast to admissible edge-dependent average dwell time (AED-ADT) methods that address switching signals, we propose admissible edge-dependent average impulsive interval (AED-AII) to deal with delayed impulses, thereby establishing the relationship between these methods and the decay rate. Meanwhile, a stabilizing controller for discrete impulsive switched linear delayed systems is proposed and the minimum average dwell time and controller gain are obtained. Compared with the previous work, the parameters of Lyapunov functional relation depend on the directed edges; the operation of subsystem is divided into asynchronous time and synchronous time, which are less conservative; the combination of AED-ADT and AED-AII can be applied to a wider range of impulsive switched systems. Finally, two examples are given to show the effectiveness of the results.

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

This paper investigates the consensus disturbance rejection problem for general linear multi-agent systems in the presence of matched disturbances under the directed communication topology. Firstly, based on the local output information among agents, the disturbance observer is proposed to estimate the disturbances and compensate for their influences on the multi-agent systems. Secondly, the fully distributed output feedback consensus protocol is designed to guarantee that all agents can reach an agreement value. Finally, a simulation example is presented to illustrate the effectiveness of the results.

In this brief, a novel distributed leader-following consensus controller for linear multi-agent systems (MASs) with one leader and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> followers is designed for optimal leader-following consensus control. A user-friendly global objective function is well designed in a quadratic form. The proper choice of the weighting matrices and necessary and sufficient conditions for optimizing the objective function are given. The proposed controller can guarantee the optimization of the objective function and the achievement of the leader-following consensus of the MASs. To deal with the coupling in the controllers, we propose a dynamic average consensus-based algorithm to estimate the controller distributedly, and the estimate errors converge to zero in finite time. A simulation example is provided to demonstrate the results.

In this paper, a new distributed model reference adaptive control (MRAC) design framework is proposed for containment control of heterogeneous uncertain multi-agent systems (MAS). Both groups of leaders and followers are considered to have general linear dynamics with the leaders subject to bounded external inputs and the followers subject to uncertain system dynamics. A novel distributed adaptive control protocol is developed under this new framework, which incorporates robust adaptive control with nonlinear compensator techniques to cope with unmeasurable bounded leaders' inputs and uncertain agent dynamics. Convergence of the containment control errors to an arbitrarily adjustable neighborhood of the origin is guaranteed based on the Lyapunov method. The proposed MRAC framework provides a promising alternative solution over the prevailing cooperative output regulation framework for heterogeneous linear MAS containment control. It enables us to handle more general system settings under more stringent control environments with limited accessibility of leaders' information and uncertain follower dynamics.

A fundamental problem in formation control is under what conditions one can design protocols for a multi-agent system to achieve desired formations. By examining the property of a class of formations that are exactly achieved in a linear multi-agent system, an interesting fact is observed that there is a connection between the achievability of desired formations and the consistency of time-varying linear equations. From the asymptotic consistency of time-varying linear equations, we propose the asymptotic consistency concept for desired formations and study its properties using the Moore-Penrose generalized inverse. With this concept, a result on achievability of desired formations is presented for linear multi-agent systems: all asymptotically consistent formations are achievable as long as the agent dynamics and communication network satisfy the controllability and connectivity conditions, respectively. We design state feedback protocols for asymptotically consistent formations using the weighted controllability Gramian and the Moore-Penrose generalized inverse. If further, the agent dynamics are observable, the observer-based protocols can be designed by the separation principle. Finally, a simulation example is given to illustrate the obtained results.