Research On Consensus Problems For Multi-agent Systems

In the past decade, the theoretical results and engineering application of coordinated control problem have been developed rapidly in various disciplines. The critical problem encountered in decentralized control of communicating-agents system is to design appropriate and effective protocols based on the task type and performance requirements of systems. Namely designing relative simple control rules specific to the agent, ultimately some key elements of multi-agent systems can achieve consensus if all agents communicate and affect with each other in accordance with the rules. The potential application value of distributed control strategies have received much attention from engineering researchers, including formation control for multiple robots, congestion control in communication networks, vehicle system and distributed sensor networks. In order to meet the requirement of engineering application, it is an urgent need to make consensus theory of decentralized control problems of multi-agent systems develop fast. At present, the theoretical framework of first-order multi-agent systems have presented in many papers. In contrast, the related theoretical results corresponding to more complicated second-order multi-agent systems are obviously inadequate. Under this background, based on algebraic graph theory, nonnegative matrix theory and Lyapunov stability theory, H_∞ consensus and group consensus for second-order multi-agent systems are studied in this thesis.1. This thesis investigates an H_∞ consensus problem for discrete-time multi-agent systems with external disturbances and time delays. By an augmentation system method as well as a system transformation technique, a reduced-order system without time delays is firstly derived. Then based on the reduced-order system, we obtain some sufficient conditions in form of linear matrix inequalities(LMIs) guaranteeing the H_∞ consensus by using Lyapunov function methods.2. This thesis addresses group consensus for multi-agent systems with switching topologies and time-varying delays, where all agents are described by discrete-time second-order dynamics. Based on the relationship between zero/nonzero in-degree graphs and nonnegative matrices group consensus criteria, which is presented in terms of easily checkable graph topology condition, is obtained for multi-agent systems with timevarying delays under switching topologies.3. In this thesis, we discuss the group consensus for continuous-time multi-agent systems, which are divided into couple groups. We first investigate the effect of the coupling strength among the agents in different groups, and obtain some sufficient conditions in form of linear matrix inequalities(LMIs) guaranteeing the group average consensus by using Lyapunov stability theories. In order to study the effect of the coupling strength, we introduce two different parameters γ1, γ2 in the network topology. Secondly, we study the same multi-agent system under two different topologies with the effect of second-order neighbors’ information. Specifically, couple-group consensus problems for multi-agent systems with different first-order and second-order neighbours’ communication delays are studied.