Consensus Problems For Multi-agent Systems With A Leader

Recently, the multi-agent distributed coordination problem has attracted many re-searchers from different disciplines including biology, physics, computer sciences and con-trol engineering. This is because that it can be widely utilized in these fields. As the basis ofthe distributed coordination problem for multi-agent systems, the consensus problem has be-come the research focus of control community. In multi-agent systems,"consensus"meansto reach a same value agreement regarding a certain quantity of interest that depends on thestate of all agents. A"consensus algorithm"is an interaction rule specifies the informationinteraction among all agents. In this paper, we focus on investigating consensus problemfor multi-agent systems with a leader, that is, leader-following consensus problem. Accord-ing to the differences properties of the leader, leader-following consensus problems can becategorized as leader-following consensus problems with a real leader and leader-followingconsensus problems with a virtual leader.The main contributions of this dissertation are summarized as follows:1. Investigation on the leader-following consensus problem on balanced graphs. In ourconsidered problem, all agents evolve on balanced information topologies. In addition,the velocity of the leader is variable and can not be measured. For such a distributedtracking problem, We first propose a coordination-variable-based(CVB) control strat-egy and attempt to investigate distributed tracking performance from a novel studyviewpoint-the collective behavior. To do so, by introducing a novel decompositionmethod, we also decompose this system into two subsystems: center tracking errorsdynamics and cohesion dynamics. Then, we find that cohesiveness in distributed track-ing problem is as important as that in swarm behaviors and introduce a new measureof cohesiveness property. Finally, we prove that our proposed control strategy cannot only estimate the tracking errors of the multi-agent system but also improve itscohesiveness by increasing cohesiveness gain independently.2. Investigation on the leader-following consensus problem with a varying-velocityleader and time-varying delays. Since the velocity of the leader cannot be measured, the reduced-order Lyapunov-Krasovskii functional in the literature cannot be extendedto our case. We consider two different cases: the leader adjacency matrix which is usedto represent the connection between the followers and the leader is time-invariant andtime-varying. For the first one, we use the decomposition method introduced in thelast sector which decomposes the group tracking dynamics into two subsystems. Thenby utilizing a Lyapunov-Krasovskii functional, we derive a sufficient condition foruniformly ultimately boundedness of the tracking errors; while for the second case,we directly use the Lyapunov-Krasovskii functional and get a sufficient condition foruniformly ultimately boundedness.3. Investigation on the leader-following consensus problem with input saturations. Aleader and all followers have bounded inputs and only move in a bounded workspace.A distributed bounded protocol is proposed for every agent to follow such leader anda sufficient condition for making every agent follow the leader is also proven.4. Investigation on the leader-following consensus problem with multiple coupled de-lays and external perturbations. In this problem, all considered agents are modeled bysecond-order integrator dynamics and both of the cases in which the directed infor-mation exchanges among all agents are fixed and switched are taken into considera-tions. First,we propose a distributed consensus protocol. By utilizing a Lyapunov-Krasovkii functional and robust performance analysis, we then obtain sufficient con-ditions for achieving consensus with a desired H∞performance.5. Investigation on the leader-following consensus problem with coupled delays and mea-surement noises. In this problem, all considered agents are modeled by second-orderintegrator dynamics and it is assumed that all noises are independent on each other.First, we propose a consensus protocol with measurement noises. By utilizing Ito?stochastic differential delay analysis method, a sufficient condition for achieving meansquare second-order consensus is obtained.