Research On Consensus Of Complex Systems

Recently, modeling and control of multi-agent systems have become focus of the study on complex systems. With the development of network communication technology, robot technique and sensor technique, lots of problems in distributed control systems have been studied. Such as flocking and swarming, formation control, distributed computing and coordinated control. In this background, the classical control theory can no more keep up with the further development of complex network systems. On the other hand, in social and economic systems there are a lot of self-organization phenomena which is the stable group behav-ior produced by interaction among agents. And the self-organization phenomena need rigorous theoretical analysis. In these reason, the multi-agent systems have attracted many researchers from different disciplines including mathematic, engi-neering technology, social sciences, biology and physics. Consensus problem is the basis of the multi-agent systems. This thesis generally researches the consensus problem of leader-follower multi-agent systems. Combined with many methods in classical control theory, some second-order protocols are proposed to realize consensus. Moreover, the coexistence of anti-phase and complete synchroniza-tion has been investigated for generalized Lorenz system. The main contents and contributions are summarized as follows:1. The thesis considers the adaptive consensus problem for leader-follower multi-agent systems. Under the condition that the interconnection graph of the agents is directed and balanced, the neighbor-based consensus protocol with adap-tive feedback gain are proposed for the follower agents to track the leader. By utilizing Lyapunov-Krasovkii functional, we then obtain a sufficient condition for achieving consensus of multi-agent systems with time-delay coupling.2. The thesis proposes an impulsive consensus protocol to solve the con-sensus problem of the second-order multi-agent systems with fixed and switching topologies. Some sufficient conditions are obtained for the states of follower agents converging to the state of leader asymptotically. Two numerical simulations are also given to verify the effectiveness of the theoretical analysis.3. In the thesis, we propose the second-order protocol to realize consensus of the leader-follower multi-agent systems with stochastic disturbance and time-delay coupling. Under the condition that the interconnection graph of the agents is directed. Based on the stability theory of stochastic delay differential equation, sufficient condition for achieving mean square second-order consensus is obtained.4. The thesis investigate a class of new synchronization phenomenon. Some control method is established to guarantee the coexistence of anti-phase and complete synchronization in the generalized Lorenz system. The efficiency of the control method is revealed by some illustrative simulations.Finally, the thesis is concluded by pointing out some further research direc-tions on the research of multi-agent systems.