Delay Margin For First-Order Unstable Multi-Agent Systems By PID-Type Control Protocol

In recent years,the consensus control problem and the containment control problem of multi-agent systems has drawn more and more attention from the control community.Consensusability means that the states of all agents eventually converge to a common state of interest under the proper control protocol.The main objective of the containment control is to design the relevant control protocol such that the followers eventually converge to the convex hull spanned by leaders.The consensus control and the containment control are basically related to both the individual agents and the interconnected topologies.In the process of information interaction among agents,there will inevitably exist time delays.It is well known that time delay generally degrades a system’s performance,and this remains so,if not more acute,for a MAS.As result,it is of great significance to study the delay margin problem of multi-agent systems with communication delay.The main results of the thesis are summarized in the following two parts:Firstly,we investigate the delay consensus margin and its bound on a class of discrete-time unstable first-order multi-agent systems with uncertain constant delay over undirected and directed fixed communication topology.In particular,we focus on the delay consensus margin achieved by two kinds of consensus protocols,one is P-type and the other is PD-type.We provide the exact expressions of the delay consensus margin and the explicit bounds by optimizing the network coupling strengths within their allowable ranges.The results show that for a strictly unstable discrete-time first-order multi-agent system,its delay consensus margin depends on the unstable pole location of each agent,as well as on the eigen-ratio of the network topology.It is also revealed that the delay consensus margin achievable by P-type consensus protocol is enlarged by PD-type protocol over undirected and directed fixed communication topology.Secondly,we investigate the containment control problem of discrete-time first-or-der unstable multi-agent systems and continuous-time first-order unstable multi-agent systems with uncertain constant delay over undirected and directed fixed communication topologies among folowers.In particular,we focus on the delay margin achieved by two kinds of containment protocols,one is P-type and the other is PD-type.We provide the exact expression of the delay margin and its explicit bound by optimizing the network coupling strengths within their allowable ranges.The results show that for a strictly unstable discrete-time first-order multi-agent system,its delay margin depends on the unstable pole location of each agent,as well as on the eigen-ratio of the network topologies.It is also revealed that the delay margin can be enlarged by PD-type containment protocol with respect to P-type one over the above two kinds of topologies.