Control And Its Optimization, Dispersion And Coordination Of The System Based On The Bmi Method

With the rapid development of modern technology and the application of project, the research of large-scale system has gained a lot of attention in the world. This is mainly because of emergence of the control problem of complex large-scale system such as electrical power system, the chemical process, the transportation, the multi-functions body, the large-scale spatial structure and the computer communication network and so on. In the traditional study of the stability and composition of large-scale system, every subsystem is always supposed stable or can be strongly stabilized through local feedback to make the large-scale system be composed by decreasing the action of interconnection relatively. In fact, the interconnection and cooperation is playing a key role in stabilizing large-scale systems.In this work, we expatiate the basic principle of decentralized control and cooperative control based on mathematic model of complex system and introduce the principle and method of the traditional large-scale systems control. Firstly, we research the decentralized stabilization problem of large-scale system based on the method of bilinear matrix inequalities (BMI) and the optimal designing problem of decentralized controller under the condition that the performance index is given. We obtain the necessary and sufficient condition to make the large-scale system can be decentralized stabilization. Moreover, we turn the designing problem of decentralized controller to the non-convex optimization problem under the restriction of BMI, and present the alternate algorithm of solving this kind of optimal problem. At last, examples indicate the conclusion's validity.Secondly, we research the linear system's interconnected stability problem and cooperative stabilization problem based on BMI and the optimal designing problem of cooperative controller when the performance index is given. A necessary and sufficient condition to make subsystems can be cooperative stabilization is obtained and turn the optimization designing problem of cooperative controller to the generalized eigenvalue minimization problem (GEVP) under the restriction of BML We also present the alternate algorithm of solving this kind of optimization problem. At last, examples indicate the conclusion's validity.Finally, the cooperative control problems of multi-body which has single-ring information structure and leader-follower information structure are discussed. Necessary and sufficient conditions are given for cooperative stabilization of the single-loop and leader-follower combined large-scale systems and the designing algorithm of cooperative controller are proposed. Similarly, examples are given to illustrate the results in the end.