Research On The Cluster Synchronization Control Of Multi-agent Systems

Due to the wide applications of multi-agent systems(MASs),the consensus/synchronization control problem of MASs has attracted considerable attention in the past few years,such as wireless sensor networks,multi-satellite system attitude control,and aircraft formation.A critical problem in this area is to design a control strategy to enable all the agents to reach an agreement on certain quantities of interest.In the actual multi-agent system,the factors that affect the consensus/synchronization behavior include not only the dynamics of the agent itself and the communication network used for information interaction,but also the external environment and physical constraints of agents,such as external disturbance and actuator saturation,etc.These factors together determine the evolution of the MASs,which should be considered as much as possible when designing the synchronization control strategies.In addition,the network is generally complex,e.g.,hierarchical and dynamic.When the network is divided into multiple interacting clusters according to the actual needs,the(completed)consensus/synchronization problem is extended to the group/cluster synchronization problem.Although fruitful and insightful results have been derived for the completed/cluster consensus problem in the sense of ideal scenarios,there are still many open problems in the consensus problem under complex environments,especially for the cluster synchronization problem.In this dissertation,we mainly focus on the cluster synchronization problem under a complex environment,including two aspects:(1)cluster synchronization problem under complex topologies;and(2)cluster synchronization problem under individual dynamics constraints.The main contents and contributions are as follows:(1)In Chapter 3,we investigate the semi-global cluster consensus for heterogeneous MASs with input saturation.A general case in a leaderless framework is studied first,and then in order to broaden the scope of application,we consider a special case in which the leader nodes are pinned intermittently.To tackle the above problems,we propose a linear control scheme by using the low gain feedback technique under the assumptions that each node is asymptotically null controllable and the underlying topology of each cluster(the extended cluster under the intermittent pinning control)has a directed spanning tree.The Lyapunov-based method and the low gain feedback technique are developed for convergence analysis.It is shown that for both cases,the convergence rate which depends on the low gain parameter and system matrices,is explicitly specified.(2)In Chapter 4,we deal with the cluster synchronization problem for heterogeneous non-linear systems with input saturation under both fixed and switching topologies.The distributed synchronization controllers are designed based on the low gain technique under the assumption that each agent is asymptotically null controllable with bounded controls(ANCBC)to deal with the input saturation.For both fixed and switching cases,the sufficient conditions for reaching the semi-global cluster synchronization are derived in terms of the solution of algebraic Riccati equation(ARE)and intra-cluster coupling strength.In addition,for the switching case,the lower bound of the total activation time on the derived topology with a directed spanning tree is explicitly specified.(3)In Chapter 5,we address the H?group consensus problem for general linear MASs with directed switching topology and external disturbance.The feasible consensus protocol is designed by Lyapunov stability theory and algebraic graph theory,and then the AREbased condition is derived to guarantee the H?group consensus.The derived conditions show that the H?group consensus problem can be solved if the multi-agent system is state feedback stabilizable with a bounded L2 gain and the appropriate intra-cluster couplings are chosen.Both the lower bound of the intra-cluster coupling strength and dwell time are explicitly specified.(4)In Chapter 6,we focus on the distributed linear quadratic optimal control problem for general linear MASs under two different directed graphs,namely the signed graph and non-negatively weighted graph.For the case of signed graph,we propose a systematic approach to design a hierarchical controller for the network involving multiple interacting clusters.By using linear-quadratic regulator(LQR)method with a properly chosen weighting matrices for the performance,an optimal hierarchical controller are derived.For the case of non-negatively weighted graph,we first derive the optimal feedback controller by using a linear operator theory-based method,aiming to guarantee the specifiedtime consensus and optimal energy-cost performance.Then,based on the optimal control law,we develop two distributed suboptimal specified-time controllers for undirected and directed graphs,respectively.Finally,to evaluate the performance of the suboptimal controllers,we derive the bounds of the energy gap between the energy consumption of the suboptimal and the optimal control laws,which can be used to improve the performance of the suboptimal control laws in the future.