Coordinative control of multi-agent networks with switching topologies and delayed communications
Student thesis: Doctoral Thesis
Related Research Unit(s)
Coordinative control problems of networked agents have attracted much attention in recent years. Their solutions rely on the algebraic graph theory and the stability theory of nonlinear systems. This thesis focuses on the leader follower architecture and consensus behavior of a group of given agents with nonlinear dynamics, for which rich studies covering the natural phenomena and engineering applications have been carried out. The thesis starts with a chapter which includes an extensive review on consensus problem in multi-agent systems, and the motivation and main contribution of this work. For readability consideration, some mathematical preliminaries are included, encompassing some key concepts in graph theory, different stability theorems for nonlinear systems especially for the retarded differential systems, and averaging theorem on time-varying systems. The first problem to be addressed is the tracking control problem of a leader-follower network over switching networks where the agent dynamics are assumed to be nonlinear and the communications between them are delayed. On the basis of common Lyapunov functional theory, our result manifests that, when the network topology is arbitrarily switching among a finite set of topologies, leader tracking can be achieved asymptotically if a set of sufficient conditions hold. Some simple corollaries applicable for delay-free case are also given. The conditions are represented via linear matrix inequalities (LMIs), and the sizes of the matrices involved are independent on the network size. Moreover, a simple optimization scheme is also formulated for determining the largest allowable coupling delay. Numerical simulations are carried out to verify the feasibility of the proposed conditions. Recognizing that the communication between the agents may be directed, and a leader may not exist, a consensus problem is further taken into account. It allows some agents to be isolated intermittently to model the case with communication failure and packet loss. In light of the multiple Lyapunov functional method and the stability of discontinuous dynamical systems, some LMI-based conditions combined with well-designed switching restrictions are established under which consensus can be ensured for nonlinear agents over switching networks. It unveils how the agent dynamics, communication delay, network topology impact on the final network dynamics. When directed topology is involved with leader following problem, in view of whether the leader is reachable for the followers, three problems for switching network and delayed communications are further explored. Accordingly, some sufficient conditions represented via LMIs are given for successful leader following. Worth mentioning is that, even when the network switches within a set of topologies of which each topology is disconnected, the followers can still track the leader if some well-designed switching rules are satisfied. To tackle the situation with time-varying topology, an averaging sufficient condition is derived for consensus problem, which reveals that, all agents can reach consensus if the network switches fast enough, and their time-averaged network can ensure consensus regardless of delayed communication and nonlinear agents' behaviors. It provides an alternative approach for studying the switching disconnected network, and the numerical simulations support the theoretical result.
- Control theory, Switching theory, Topology, Multiagent systems