Research On Control For Consensus Of Multi-Agent Systems And Synchronization Of Complex Dynamical Networks

As important research topics in complexity scicence, multi-agent systems and complex dynamical networks have been in the forefront of in many fields. Recently, they have attracted many scholars from control science, mathematics, physics, biology, robotics, social sciences, economics, management, medicine and so on. Research on control for multi-agent systems and complex dynamical networks is not only important for theoretical researches, but slao contributive for practical applications. By means of several tools from control theory, algebraic graph, matrix theory and partial differential equations, the leader-following consensus in multi-agent systems and synchronization problem of complex dynamical networks are investigated in this paper. The main work of this paper can be summarized as follows:1. The sufficient conditions guaranteeing leader-following consensus, based on Lypunov stability theory, are obtained for multi-agent systems in which the controlling effect of each follower depends on its own state. With the assumption of the followers’positive initial states, control protocols are designed. For the network with fixed or switching topologies, and undirected information flow, the leader-following consensus of the systems can be achieved if the interaction topology among agents is connected. Moreover, for the network with directed information flow and communication time-delays, the leader-following consensus of the systems can be realized if the leader is "globally reachable". Finally, Some numerical examples illustrate the effectiveness of the theoretical results.2. The problem on leader-following consensus is discussed for multi-agent systems in which the state of agents in multi-agent systems changing over time and space, and the influence of diffusion among followers is taken into account. When the controlling effect of each follower depends on its own state, a control protocol is proposed. If the interaction undirected topology among agents is connected, with some assumption of the followers’ initial states, the sufficient conditions guaranteeing the leader-following consensus under the proposed control protocol are provided by use of algebraic graph theory, the method of energy estimates and Sobolev embedding theorem. Finally, the simulation results of two examples are presented to demonstrate the effectiveness of the theoretical results.3. Master-slave synchronization of chaotic systems with perturbations under a nonlinear control scheme is investgated. The sufficient conditions guaranteeing master-slave synchronization of systems without perturbation or with vanishing perturbations are proposed, respectively; The sufficient conditions guaranteeing master-slave approximate synchronization of systems with nonvanishing perturbations are also proposed. Finally, several simulations for Lorenz system are provided to verify the effectiveness and feasibility of our method. It can be found that the control scheme in this paper is sharper than the existing ones in literatures.4. Synchronization problem for general coupling complex networks with time varying delay is studied. The restriction on the out-coupling matrix of a dynamical network that is always assumed to be symmetric or irreducible is eliminated. Complex eigenvalues for the general out-coupling matrix are considered and complex vectors are handled accordingly. Based on Lyapunov stability theory, the matrix decomposition technique and linear matrix inequalities(LMIs), the sufficient conditions guaranteeing synchronization are given by constructing Lyapunov-Krasovskii functions. Some numerical examples illustrate the effectiveness of the theoretical results. The results show much less conservative than the existing ones in literatures.5. Based on the community structure of the networks, a local linear control strategy is proposed for the cluster synchronization problem of complex dynamical networks with each node being a Lurie system. With the aid of Lyapunov stability theory, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks in time-domain and frequency-domain, respectively. The notion of the cluster synchronized region is introduced, and necessary and sufficient conditions guaranteeing the unbounded cluster synchronized region are derived. Furthermore, the cluster synchronization and the cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Some numerical examples illustrate the effectiveness of the theoretical results.