Research On Consensus Problems Of Multi-Agent Systems Under Network Environments

In recent years, more and more researchers have focused their attention on the distributed coordinated control of multi-agent systems. This is due to its ability of revealing emergence properties of many natural complex systems and broad applications in engineering. Consensus plays a critical role in the distributed coordinated control of multi-agent systems. To achieve the consensus, each agent needs to exchange the local information with its neighbor agents. Note that multi-agent systems are in complex network environments, agents might suffer from external attacks, resulting in the interruption of the local information exchange with their neighbors, and the local information exchange among agents is corrupted by communication delays and measurement noises. All of external attacks, communication delays and measurement noises might lead to the unachievement of consensus. Thus, it is necessary to analyze the effects of these three factors on consensus and to find some strategies to reduce the effects.In this dissertation, from the synthesis point of view, we investigate how to reduce the effects of external attacks, communication delays and measurement noises on consensus with the aim to improve the robustness of multi-agent systems against these three factors. Main contributions of this dissertation are as follows:First we investigate cascading failures of large-scale multi-agent networks under external attacks from the perspective of complex networks. Using the average two-step degree to measure the heterogeneity of networks, we propose the network design problem about the scale-free network with the optimal robustness against external attacks. Compared with the entropy of the degree distribution, the average two-step degree contains not only the information about the diversity of the degree distribution but also one about the network topology. Second we study the problems about the connectivity recovery of multi-agent networks having suffered from external attacks, propose the strategy of connecting neighbor set to recover the connectivity of the resulting interconnection network, analyze the effects of the strategy on the robustness to next external attacks and the convergence speed of achieving consensus, and give the corresponding optimization problems about the network design. Different from the existing results, from the synthesis point of view, we investigate the connectivity recovery.By introducing the delayed-state-derivative feedback and weighted average prediction into the traditional delayed consensus protocols, we partially solve the contradictions between the robustness to communication delays and the convergence speed of achieving consensus in first-order delayed multi-agent systems with undirected topology and second-order delayed multi-agent systems with directed topology. It is proved that for first-order supercritical-delay multi-agent systems and two kinds of second-order delayed multi-agent systems, introducing the delayed-state-derivative feedback with the proper intensity and the weighted average prediction with the proper length into the traditional delayed consensus protocols can simultaneously improve the robustness to communication delays and the convergence speed of achieving consensus.We consider the sampled-data-based consensus tracking problems of first-and second-order multi-agent systems with measurement noises. For the case of sampling delay, the probability limit theory, algebra graph theory and some other technologies are employed to derive the sufficient and (or) necessary conditions guaranteeing the mean square bounded consensus tracking. For the case of communication delays, the delay decomposition technology, the augmented matrix method and some other technologies are employed to derive the sufficient and (or) necessary conditions guaranteeing the mean square bounded consensus tracking.