Consistency Analysis And Control Of Multi- Interconnected Complex Dynamic Networks

The complex network is an important research topic of today’s scientific community,which highly summarize the complex network system. The consensus problem is widespread in all kinds of complex dynamic network system, which is the typical collective behavior of complex dynamic network, and it is also one of the most important dynamic characteristics of complex networks. The basic purpose of consensus problem is to make the multi-agent system achieve the consistent state according to the local information. So the consensus problem of multi-agent system is an important topic of the coordination control. This thesis addresses the consensus problem for dynamic network system with multi-interconnection of multi-agent communication in fixed topology and Markov stochastic jump topology, then we give the system consistency criterion and design the static output feedback controller. The main work of this thesis are as following :(1) For the dynamic network system with state and controller interconnections, the consensus problem is concerned. Based on the stability theory of partial variables, the linear transformation matrix is used to deal with the consensus problem, and we convert the consensus problem to the partial stability problem. Considering the state and controller interconnections with the same structure, we make the stability problem of the dynamic networks system decompose into several independent linear system stability problems. By using Lyapunov method and the projection theorem, we give the consistency criterion in the LMI form, and the static output feedback controller parameters are obtained by using the criterion. Furthermore, the consensus problem of linear dynamic network system with multi-interconnections and parameter uncertainties are considered. The consistency criterion based on LMI is given and the method of the static output feedback controller is also designed.(2) The consensus problem of nonlinear dynamic network system with linear and nonlinear interconnections is addressed, and the node system is a nonlinear system with Lure type that contains the linear part and the nonlinear function which satisfies the condition of a certain sector. We use linear transformation matrix as(1) to convert the consensus problem to partial stability problem. Based on the circle criterion, frequency domain criterion is obtained, then we use KYP lemma and Schur lemma to get the time domain criterion in the LMI form and the method of the static output feedback controller is proposed. Meanwhile the system with interconnection uncertainty and nonlinear uncertainty are taken into account. We obtained the relevant frequency domain criterion, The time domain criterion in LMI form is also given. What’s more, the method of static output feedback controller is presented.(3) The consensus problem of multi-connected dynamic network systems with communication delay and Markov stochastic jump topology is investigated. Without loss of generality, we choose the jump speed rate matix is partly unknown. First of all, we apply the linear transformation matrix in(1) to solve the consensus problem, and we converted the consensus problem into a problem of partial stability. Then under the each mode of the system, we choose the appropriate Lyapunov Krasovskii functionals to get the consistency criterions in bilinear matrix inequalities form of linear and nonlinear systems, respectively. And by using iterative algorithm, the static output feedback controller’s gain matrix is obtained.