Event‐triggered Guaranteed Cost Consensus of Networked Singular Multi‐agent Systems

The problem of event‐triggered guaranteed cost consensus of discrete‐time singular multi‐agent systems with switching topologies is investigated in this paper. To save the limited network communication bandwidth of multi‐agent systems, a novel event‐triggered networked consensus mechanism is proposed. Based on the graph theory and singular system theory, sufficient conditions of guaranteed‐cost consensus of discrete‐time singular multi‐agent systems are derived and given in the form of the linear matrix inequalities, respectively. A co‐design approach of the multi‐agent consensus gain matrix and the event‐triggered parameters is presented. Furthermore, based on the approach of second class equivalent transformation for singular systems, the cost function is determined, and an explicit expression of consensus functions is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Second‐order consensus for directed multi‐agent systems with sampled data

This paper deals with the consensus problem of second‐order multi‐agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi‐agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time‐varying piecewise‐continuous delay and proposing a novel time‐dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Bipartite Linear χ‐Consensus of Double‐Integrator Multi‐Agent Systems With Measurement Noise

The bipartite consensus problem is investigated for double‐integrator multi‐agent systems in the presence of measurement noise. A distributed protocol with time‐varying consensus gain is proposed. By using tools of state transition matrix and algebraic graph theory, necessary and sufficient conditions for the designed protocol to be a mean square bipartite linear χ‐consensus protocol are given. It is shown that the signed digraph being structurally balanced and having a spanning tree are not only sufficient, but also necessary for bipartite consensus. Furthermore, the protocol is proved to be a mean square bipartite average consensus protocol if the signed graph is weight balanced.     

Admissible Consensus of Multi‐Agent Singular Systems

Consensus problems are studied for both continuous‐time and discrete‐time multi‐agent singular systems with time‐invariant and directed communication topologies. Under restricted system equivalence of singular agents, sufficient and necessary conditions are obtained for admissible consensus ability with static protocols, which are based on both the relative information of the dynamic states and the absolute information of the static states. For a network of continuous‐time singular systems, the existence of admissible consensualization can be cast into strong stabilizability of the agent dynamics. Once discrete‐time multi‐agent singular systems satisfy the condition of reaching nontrivial final consensus states, strong stabilizability is a sufficient condition to achieve admissible consensualization. Two algorithms are proposed to construct two protocols, which are based on a linear matrix inequality and a modified Riccati equation, respectively. Finally, the algorithms are illustrated by two simulation examples.     

Robust consensus tracking for a class of high‐order multi‐agent systems

In this paper, we study the robust consensus tracking problem for a class of high‐order multi‐agent systems with unmodelled dynamics and unknown disturbances. A continuous robust state feedback control algorithm is proposed to enable the agents to achieve robust consensus tracking of a desired trajectory. By utilizing Lyapunov analysis methods and an invariance‐like theorem, sufficient conditions for semi‐global asymptotic consensus tracking are established. A robust output feedback control algorithm is designed to obtain a uniformly ultimately bounded consensus tracking result. Numerical simulations are provided to show the effectiveness of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

The consensus problem is investigated in this paper for a class of multi‐agent systems with general linear node dynamics and directed communication topologies. A new distributed observer‐type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer‐type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi‐agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low‐Earth‐orbit satellite formation flying are provided to illustrate the theoretical results.     

Consensus of Fractional‐Order Uncertain Multi‐Agent Systems Based on Output Feedback

This paper is devoted to the consensus protocol design for a set of agents with fractional‐order uncertainty dynamics where the fractional order α satisfies 0 < α < 2. For multi‐agent systems (MASs) with fixed undirected topology, a distributed static output feedback protocol is proposed with an undetermined system matrix. Based on model transformation and fractional‐order stability theory, sufficient conditions are derived to ensure the consensus of MASs in terms of linear matrix inequalities (LMIs). Finally, a simulation example is employed to validate the effectiveness of the proposed consensus protocol.     

Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data

This paper addresses the distributed observer‐based consensus problem of second‐order multi‐agent systems via sampled data. Firstly, for the case of fixed topology, a velocity‐independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed Consensus of Third‐order Multi‐agent Systems with Communication Delay

This paper studies the consensus problem for a class of general third‐order multi‐agent systems on an undirected connected network. By employing a variables transformation, the consensus control problem can be turned into a asymptotical stability problem. Then we present a necessary and sufficient condition for guaranteeing consensus by using Routh‐Hurwitz stability criterion. And this result can be applied to a special case of third‐order integrator systems. Also we will present a tolerable communication time delay for third‐order integrator systems under the assumption that multi‐agent systems can reach consensus without communication delay.     

Robust and nonfragile consensus of positive multiagent systems via observer‐based output‐feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer‐based dynamic output‐feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state‐feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state‐feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state‐feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.     

Suboptimal Output Consensus for Time‐Delayed Singular Multi‐Agent Systems

The current paper investigates guaranteed‐cost output consensus analysis and design problems for high‐order linear time‐invariant singular multi‐agent systems with constant time delays, which can realize suboptimal output consensus control. Firstly, a new output consensus protocol with a suboptimal index and a single delay is proposed to realize the tradeoff design between output consensus regulation performances and control energy consumptions. Then, sufficient conditions for guaranteed‐cost output consensus and consensualization are derived in terms of linear matrix inequalities by a combined tool from the Lyapunov‐Krasovskii approach and the free‐weighting matrix technique, respectively, and the output consensus function is determined on the basis of the First Equivalent Form. Finally, a numerical example is performed to demonstrate the effectiveness and conservativeness of theoretical results.     

LQR‐based optimal topology of leader‐following consensus

In this paper, we consider the optimal topology for leader‐following consensus problem of continuous‐time and discrete‐time multi‐agent systems based on linear quadratic regulator theory. For the first‐order multi‐agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second‐order multi‐agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second‐order leader‐following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Node‐to‐node consensus of multi‐agent networks with event‐triggered control and packet losses

This paper studies the node‐to‐node consensus problem for multi‐agent networks possessing a leaders' layer and a followers' layer via the pinning control. In order to realize the consensus and reduce the update frequency of the controller, a suitable event‐triggered mechanism is introduced into the control strategy. Furthermore, the phenomenon of packet loss is considered in the designed controller. Based on the M‐matrix theory and Lyapunov stability theory, this paper presents the sufficient conditions for the node‐to‐node consensus of networks. Meanwhile, it is proved that the Zeno behaviour is excluded. Finally, two numerical simulations are provided to demonstrate the effectiveness of the theoretical results.     

Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

This paper is concerned with the fixed‐time coordinated tracking problem for a class of nonlinear multi‐agent systems under detail‐balanced directed communication graphs. Different from conventional finite‐time coordinated tracking strategies, the fixed‐time approach developed in this paper guarantees that a settling time bound is prescribed without dependence on initial states of agents. First, for the case of a single leader, a distributed protocol based on fixed‐time stability techniques is proposed for each follower to accomplish the consensus tracking in a fixed time. Second, in the presence of multiple leaders, a new distributed protocol is proposed such that states of followers converge to the dynamic convex hull spanned by those of leaders in a fixed time. In addition, for a class of linear multi‐agent systems, sufficient conditions that guarantee the fixed‐time coordinated tracking are provided. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.     

Consensus of heterogeneous first‐ and second‐order multi‐agent systems with directed communication topologies

In this paper, we consider the consensus problem for heterogeneous multi‐agent systems composed of some first‐order and some second‐order dynamic agents in directed communication graphs. Consensus protocols are proposed for the second‐ and first‐order dynamic agents, respectively. Under certain assumptions on the control parameters, for fixed communication topologies, necessary and sufficient conditions for consensus are given, and the consensus values of all agents are established. For switching topologies, sufficient conditions are given for all agents to reach consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Coordination of discrete‐time multi‐agent systems via relative output feedback

This paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete‐time multi‐agent systems via relative output feedback. An observer‐based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi‐agent systems with discrete‐time double integrator dynamics are discussed where a simple control protocol directly using two‐step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation‐based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust output consensus for a class of fractional‐order interval multi‐agent systems

This paper is devoted to the robust output consensus problem of fractional‐order interval multi‐agent systems (FOIMASs) with fixed undirected topologies, where the fractional order, the system matrix, and the input matrix are perturbed simultaneously, and there exist linear coupling relationships among the fractional order and the perturbations of the system matrix and the input matrix. According to the information of the agents' neighbors, we design a distributed output feedback protocol. A sufficient condition guaranteeing the robust output consensus of FOIMASs is derived in terms of nonlinear matrix inequalities. By the matrix transformation and the singular value decomposition, the nonlinear matrix inequalities are transformed into linear matrix inequalities, and the output feedback gain matrix is obtained. A numerical simulation example is presented to demonstrate the effectiveness of the proposed method.     

L2 − L∞ Consensus Control for High‐Order Multi‐Agent Systems with Nonuniform Time‐Varying Delays

This paper considers consensus problem for high‐order multi‐agent systems with dynamically changing topologies and nonuniform time‐varying delays. By means of the tree‐type transformation approach, the model transformation is conducted and the consensus problem is converted into an L₂ ? L_∞ control problem of equivalent reduced‐order systems. Furthermore, a Lyapunov‐Krasovkii function is constructed for stability analysis and sufficient conditions in terms of linear matrix inequalities are derived to ensure the consensus with the prescribed L₂ ? L_∞ performance. A numerical simulation is provided to verify the correctness of the theoretical results.     

Consensus of Delayed Multi‐agent Systems via Intermittent Impulsive Control

A novel intermittent impulsive scheme is presented to realize consensus of multi‐agent systems with time‐varying delay in this paper because intermittent impulsive control may break through the limitation of upper bound of impulsive intervals in general impulsive control in our consensus scheme. Instead of activating all the time, we introduce the intermittent impulsive control approach into the delayed multi‐agent systems where the impulsive controller is only functioned in the control windows. Based on the algebraic graph theory, the Lyapunov stability theory, and Halanay inequality matrix theory, some adequate conditions are proposed to guarantee the consensus of delayed multi‐agent systems via pinning intermittent impulsive control. Simulation results are provided ultimately to verify the validity of the proposed control mechanism.     

Consensus of data‐sampled multi‐agent systems with Markovian switching topologies

This paper studies the consensus problem of data‐sampled multi‐agent systems with Markovian switching topologies. Two different consensus algorithms are considered. By a system transformation, the mean‐square consensus problem of multi‐agent systems is converted into the mean‐square stability problem of Markov jump systems. Necessary and sufficient conditions of mean‐square consensus are obtained. The cone complementary linearization algorithm is used to get the allowable control gain. Simulation examples are given to show the effectiveness of the results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society