Stabilizability And Containment Control Of Discrete-time Multi-agent Systems

The reserach of multi-agent system is a comprehensive subject which is based on the theoretical tools of mathematics and the application background of the control.Coordination control of multi-agent system has been a hot topic in the field of system control.By combining matrix theory,control theory,stability theory and algebraic graph theory together,stabilizability and containment control problems of multi-agent systems are studied.The main results and contributions include the following points.First,the problem of stabilizability for general discrete-time linear multi-agent systems is studied.For fixed topology,a necessary and sufficient graph-theoretic condition is presented for stabilizability of multi-agent systems.Based on this,a general linear form of the external control input is given,and two methods to design the feedback gain matrix by Riccati equality/inequality are proposed.For switching topology,a sufficient graph-theoretic condition is presented,under which the stabilizability of multi-agent systems is achieved by introducing an averaging analysis approach.Finally,both results under fixed and switching topologies are applied to solving the problems of tracking and formation control of discrete-time multi-agent systems,and some sufficient and/or necessary conditions are presented.Second,this paper studies the containment control problem for the switched multi-agent system which is composed of continuous-time(CT)and discrete-time(DT)subsystems.Interactions among agents in CT and DT subsystems are modeled by different digraphs.In the stationary leaders case,sufficient conditions are considered when the followers are first and a second order integrators,respectively.When the followers are first-order integrators,the containment control problem is solved by introducing the SIA matrix and analyzing the system transfer matrix at different time intervals.When the follower are second-order integrators,the second-order integrator model is transformed into a first-order integrator model by introducing virtual intelligent agent.By using algebraic theory and graph theory,some conditions which guarantee the achievement of containment control are established.In the dynamic leaders case,not only the followers will move into the convex hull but also the leaders will converge to the desired formation by having the leaders use the consensus formation protocol and the followers use the general consensus protocol.Finally,in the environment of Window 7,the simulation results are given to verify the effectiveness of our theoretical results by Matlab.