Optimal Control Of Hybrid Dynamic Systems And Its Application In Robot Control

Hybrid dynamical systems (HDS) are a class of dynamical systems that are made up of some continuous variable process and some discrete event process which occur alternately and interact. Based on impulsive model,switched model and impulsive switched model, this thesis mainly studies optimal control problem of hybrid systems with hybrid controls. The application of switched systems to robot control is experimented. Firstly, background and signification of HDS are reviewed,and the reported research works on HDS and optimal control of HDS are summarized. Based on industrial applications such as macroeconomic systems and manufacturing, a new mathematic model, the impulsive switched system with hybrid control, is presented for the systems under piecewise continuous control and impulsive discrete control at the switching instants. This thesis begins the real research from studying the controllability of the linear impulsive system with or without disturbance. After that, the quadratic optimization problem of the linear impulsive system is studied and a hybrid feedback controller is designed. Then, the method of hybrid feedback is extended to the optimal control of the impulsive switched system with hybrid control. This thesis also studies how to get optimal switching instants of the impulsive switched system and optimal problem of nonlinear switched system with constrains. Finally, the application of hybrid system to robot control is experimented simply. In the end, a brief summary has been done for the discussion and the farther research trend on optimal control of hybrid dynamic systems is presented.