On Consensus Of Multi-agent Networks

Multi-agent network is a new and emerging scientific discipline that has attracted great attention in many fields of science. The consensus and stability problem of complex net-works are main dynamic behaviors of the actual dynamic systems. They are also very impor-tant and significate in the actual applications. Hence, the study of distributed collaborative control of multi-agent networks is not only to reveal inner rules of the nature phenomenon, the more important is to guide our work and life better and service for the human society through obtaining the more inherent law of the nature phenomenon. The distributed collab-orative control of multi-agent systems has been widely used in many fields.Many coordination control tasks can be united to the same theory structure—the con-sensus problem of multi-agent networks, therefore this dissertation studies the consensus problem of multi-agent networks. In many applications involving multiagent/multivehicle systems, groups of agents need to agree upon certain quantities of interest. Such quantities might or might not be related to the motion of the individual agents. As a result, it is impor-tant to address agreement problems in their general form for networks of dynamic agents with directed information flow under link failure and creation. Consensus problems have a long history in the field of computer science, particularly in automata theory and distributed computation. To achieve a consensus, intelligent between body need to undertake local in-formation exchange. It need to exchange the information between neighboring agents. Usu-ally, the actual multi-agent systems are often in the complex network environments, such as the system or the agent may be attacked by the external disturbance, the connection may be broken and so on. Correspondingly, there are communication delay and measurement noises in the information transmission. Based on the existing research results, this paper studies the consensus problems of the multi-agent systems with the complex dynamic net-work much more thoroughly and systematically by using the control theory, stability theory, algebra graph theory, hybrid system theory and the homogeneity with dilation. The main contents of this dissertation are given in the following.This dissertation studies the mean-square average consensus for the multi-agent sys-tems with time delay in the measurement noises environment first. By combining the tools of algebraic graph theory, matrix theory and stochastic analysis, consensus protocols for the multi-agent systems with measurement noise and time delay are elaborately analyzed. The example and simulation results are given to illustrate the effectiveness of the obtained theo-retical results. Moreover, the simulations demonstrate that, the proper consensus-gain func-tion in the consensus protocol is the necessary and sufficient condition for the convergence of the multi-agent systems. Random network means that the existence of any edge is prob-abilistic and independent of any other edge. Next, this dissertation studies the convergence and convergence speed for the second-order and the high-order discrete-time multi-agent systems with random network and arbitrary weights. By introducing the agreement set, velocity control gain and high-order state control gain, some consensus protocols are pro-vided for the discrete-time random network. Moreover, the per-step convergence factor and asymptotic convergence factor are proposed to measure the convergence and convergence speed.However, it is often required that the consensus can be reached in finite time, such as when the control accuracy is crucial. Thus the study of the finite-time consensus for the networks is not only theoretically interesting but also practically important. The finite-time consensus problems of first-order and second-order multi-agent systems under fixed and switching network topologies are studied. Based on the graph theory, LaSalle's invari-ance principle and the homogeneity with dilation, the finite-time consensus protocol of each agent using local information is designed. Moreover, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results. The finite-time consensus problem of the multi-agent system with switching jointly connected topologies is also studied. Some sufficient conditions are derived for the consensus protocols even though the communication links between the agents dynamically change over time and the corresponding graphs may be unconnected. Ultimately, the consensus of the mixed-order multi-agent networks which contain both first-order and second-order agents are studied by designing the impulse control protocols. The necessary and sufficient condition are obtained to ensure the consensus of the mixed-order networks.Finally, a summary has been done for all discussions in the dissertation. The further and more deeply researching works are presented for the problem of the multi-agent systems.