On Impulsive Consensus Of Multi-agent Systems And Its Dynamics

The consensus problem of multi-agent systems has wide application prospect and is one of current international topics in the field of control theory and application. This dissertation investigated the consensus problem of multi-agent systems mainly based on graph theory, random matrix theory and control theory and devoted to solve the related isslues. The synchronization and dynamics of impulsive coupled nonlinear systems are important research contents in the current international dynamics and control field. This dissertation investigated the synchronizaiton of a class of impulsive coupled systems based on contraction theory and studied the complex dynamics and its bifurcation mechanism of a class of impulsive coupled Duffing oscillators. This work has important significance in improving the theory of multi-agent systems and impulsive systems and its application in practice. The basic contents of this dissertation are given as following:The research background, current research status of the consensus problem of multi-agent systems, non-smooth systems and impulsive systems are given firstly in the chapter 1. Then the significance of this research and the structure of the dissertation are introduced.Now continuous control protocols are received much attention, however other forms of control protocols have received relatively little attention. In chapter 2, we introduce impulsive control protocols for multi-agent linear dynamic systems. The impulsive control protocols need low-cost and can easily implement. Sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered.The third chapter investigates the impulsive consensus of multi-agent nonlinear systems on the basis of chapter 2. The third chapter is divided into two parts based on the topology of the network. In the first part, we investigate the problem of impulsive consensus of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. In the second part, we investigate the problem of impulsive consensus of multi-agent systems for directed networks with switching topologies, where each agent can be modeled as an identical nonlinear system. Then sufficient conditions are given to guarantee the consensus of the multi-agent system based on the stochastic matrices theory. When the topologies of the networks are switching and each graph is strongly connected and balanced, the scheme to design the impulsive control protocol is proposed.The passivity approach is a nice tool for controlling interconnection systems. In chapter 4, we study the problem of impulsive output consensus of multi-agent dynamical systems, where each agent is a passive system. Based on the passive theory of impulsive systems, sufficient conditions are given to guarantee the output consensus of the multi-agent systems in two cases that the network is fixed and the topologies of networks are switching. The equations of agents need to be identical in chapter 2 and chapter 3, however, The equations of agents need not to be identical when the agents are passive.Impulsively coupled oscillators which are assumed to interact with each other only at discrete times have been utilized for various image processing applications and so on. In chapter 5, we investigate the synchronization problem of impulsively coupled oscillators based on the contraction theory. Contraction analysis of two impulsively coupled oscillators and networked impulsively coupled oscillators is provided based on the proposed partial contraction theory of impulsive systems, respectively. Sufficient conditions for synchronization of impulsively coupled oscillators are derived.The nonlinear systems with periodic impulsive forces are non-smooth systems and have complex dynamics. In chapter 6, the complex dynamics of Chen system with periodic impulsive forces is investigated and the Floquet theory is used to explore the non-smooth bifurcation mechanism for the periodic solutions. The non-smooth bifurcation of Chen system with periodic impulsive forces is analyzed. The system can evolve to chaos by a cascading of period-doubling bifurcations. Besides, the system can evolve to chaos immediately by saddle-node bifurcations from periodic solutions.Impulsively coupled systems are high dimensional non-smooth systems and have rich and complex dynamics. In chapter 7, the complex dynamics of the non-smooth system which is unidirectionally impusively coupled by three Duffing oscillators in ring structure is investigated. By constructing a Poincar6 mapping, we get the bifurcation condition, and give analytical expression of Jacobi mapping matrix of Poincare map. Then we obatin the bifurcation set and Floquet characteristic multipliers by the shooting method and the Runge-Kutta method. When the period is fxed and the coupling strength changes, the system experiences stable solution, periodic solution, Quasi-periodic solutions, hyper-chaotic, etc. The Floquet theory is used to study the stability of the periodic solutions of the system and some classic bifurcation.In chapter 8, some meaningful results are summarized. Also some existing problems as well as the future work are pointed out.