The Switching Control Of Nonlinear System And Its Optimization Research

A switched (Switched Systems) system is an important class of hybrid systems.The study was derived from research on hybrid systems. Switching system consists ofseveral subsystems, each subsystem may be discrete, might also be continuous. In theprocess of system operation, each time only a subset of the system in action, while theother subsystem does not work. Therefore, switching rules in the operation of theswitching system is very important, the system in a moment in which sub system,depends entirely on the switching rules. Switching system may exist both continuousdynamics and discrete switched signals, and the two signals mutual influence,interaction, so that it has a very complex dynamic behavior and abundant contents.Therefore, switching systems in many areas are used, such as power system, acomputer disk drive, robot control, traffic management, car pendulum control system,and applied widely in engineering partition PID, fuzzy controlling, all belong to thecategory of switching system. Therefore, switching system for general hybrid systemalso has a theoretical guidance and practical significance.In reality, most control systems are nonlinear system. Nonlinear is a common,widespread phenomenon. While the phenomenon of the linear systems only relative,special existence of an ideal. A nonlinear switched system is a typical form of thenonlinear system. In view of this kind of system control problem is worthy of ourin-depth study.This thesis according to the model of known nonlinear reversible switchingsystem, put forward the linearization method of switched nonlinear system based onthe inverse system, to realization inverse system by using the structural engineeringmethod, to make the object been controlled right inverse system became to lineartransfer relationship and has been decoupled by composite pseudo linear system,designed a additional closed-loop controller for comprehensive. According to thetheory above, the closed loop controller also been designed. For the model unknownnonlinear reversible switching system, put forward the linearization method based onneural network inverse system of nonlinear switched systems, by using the integratorand neural network inverse system of the controlled system in inaccurate charged withthe mathematical model and parameters do not have to give the analytical expressionsof the inverse system, just to prove the reversibility of the controlled system based onimplementation charged with linearization and decoupling of the system, and gives the closed-loop controller design algorithm. For a class of nonlinear switched systems,the subsystems of which contain discrete time delay item by the approximatelinearization method, the asymptotic stability problem is studied. As long as thecorresponding parameters meet convex combination conditions and the correspondingpositive definite symmetric matrix meets the appropriate constraints of linear matrixinequality, the switch program exists for any switching signal. With the control ofswitch program, this type of switched systems is asymptotically stable, and it isproved. By introducing a matrix, the constraint quadratic converts to theunconstrained quadratic, and the sufficient condition that the type of switched systemis asymptotically stable is given with the multiple Lyapunov Function method. For theoptimal control problem of nonlinear switched systems, genetic PID optimal controlmethod is proposed by combining traditional PID controller and genetic algorithm(GA). And this algorithm is known as the GAPID control method. At the same time,gives the corresponding simulation example, provide analytical results.