Analysis And Control For Asymptotic Behaviors Of Complex Dynamic Systems

Complex dynamic systems widely exist in nature and many application fields. They are either some groups that consist of numerous interacting individuals, or some nonlinear systems with unpredictable states. Due to their important applications in the fields of engineering, national defense, medicine, information security, etc, complex dynamic systems have drawn a lot of scholars’ attention. Owning to the complicated internal conditions of the systems, a lot of interesting behaviors gradually emerge. Describing the asymptotic behaviors exactly and revealing the inherent rules of the behaviors of complex dynamic systems help us understand the real world. More importantly, it is also conducive to practical applications. Research on complex dynamic systems combined with networks is a new direction in recent years, and also becomes new focus in disciplines like mathematics, physics, biology, economics, control science, etc. This dissertation studies the asymptotic behaviors of networked multi-agent systems, complex dynamic networks and nonlinear systems.Recent studies mostly focus on the single-asymptotic-behavior problems of networked multi-agent systems, such as consensus, one object tracking. While it doesn’t demand a system in nature and some application fields reach one agreement sometimes. Based on these considerations, multiple coordination (namely, multiple asymptotic behaviors) problems of networked of multi-agent systems are studied here. This dissertation also studies the synchronization of complex dynamic networks in considering communication constraints on the network. In addition, recognizing the chaotic encryption plays an important role in information security, this dissertation studies chaotic behaviors of nonlinear systems. The main contents of this dissertation are stated as follows.With the consideration of nonlinear feature in the process of information transmission, a nonlinear protocol is proposed for the networked multi-agent systems. And multi-consensus of nonlinearly networked multi-agent systems is investigated. By using graph theory, matrix theory and the method of Lyapunov functions, a sufficient condition for the networked multi-agent systems to achieve multi-consensus is derived. And the agreement of each group is studied. A feedback controller for the networked multi-agent systems is then designed to drive the system to achieve multi-consensus. The results reveal the relationships among the initial states, the topology of the network, multi-consensus behaviors and states.For the communication might be periodic rather than continuous sometimes, impulsive protocols with sampled information are used to solve a containment control problem for second-order networked multi-agent systems with several leaders. In the case of stationary leaders, by analyzing the eigenvalues of a matrix and using the bilinear transformation theorem, a necessary and sufficient condition for the systems to achieve containment control is derived. In the case of dynamic leaders with fixed velocities, by calculating a limitation, a sufficient condition for the systems to achieve containment control is given. Numerical simulations illustrate the effectiveness of the theoretical results. The results reveal the relationships among the impulsive protocol, initial states, the topology of the network, containment control behaviors and states.In view of multiple objectives existing in tracking problems and their incomplete information to the followers, two communication protocols are proposed in terms of the relative position information and the estimated acceleration. And set tracking problems of networked multi-agent systems with several objectives are studied. In case of the fixed and the switched topology respectively, by using Lyapunov function, a sufficient condition for the systems to achieve multi-objective tracking is derived. The results can deduce to containment control problems. It suggests that set tracking can be achieved asymptotically if the network contains a directed spanning forest, and the parameters of the protocol and the smallest eigenvalue of the Laplacian matrix satisfy an inequality.Since the coupling delay between two nodes not only varies with time but also differs from other coupling delays, one kind of complex dynamic networks with diversely coupling delays is proposed. And the synchronization problem of this type of networks is investigated. Based on some assumptions, an effective sufficient condition of global synchronization is derived by using graph theory, the method of Lyapunov-Krasovskii function, etc. The result provides a judgment for the networks achieve synchronization.Some novel three-dimensional quadratic autonomous chaotic attractors are presented. By constructing a series of nonlinear systems and simulating them,27chaotic attractors are found. The basic dynamical properties of one attractor, as an example, are investigated in details, including equilibria, Jacobian matrices, Lyapunov exponents, fractal dimension, dissipativity, together with dynamical waveform in time domain, frequency spectrum and Poincar’e mapping. The oscillator circuit of the new chaotic system is afterwards designed by using EWB software and a typical chaotic attractor is experimentally demonstrated.