Studies On Optiaml Control For Hybrid Systems

Hybrid systems (HS) are real-time systems that react to both Continuous and discrete activities. Theory of hybrid systems is mainly product of combination of computer science and control theory. The occurrence and the development of hybrid system are both the demand of theory and practice, and the inevitable outcome of the development of control theory, system theory, computer technology and mathematics. The research of hybrid systems is demand of further development of traditional control theory and it bridges various subjects such as mathematics, system theory and computer science. Also, the investigation of hybrid systems proposes series of new and challenging problems. Hybrid systems are highly nonlinear complicated systems whose states evolve with both run time and event. From the control point of view, this dissertation investigates the detail of optimal control of hybrid systems. The main contributions of the dissertation are as follows: (1) The definition of hybrid systems is presented firstly, and then explains the emergency and development process of hybrid system from two sides, control theory and computer technology. For the complication of the hybrid systems and the different background and interest of researcher, there are various contents, methods and results about hybrid system. The present achievement and situation of hybrid system research are summarized and analyzed in detail, and then some difficulties and problem both in theory and in practice to be resolved are listed out. (2) Based on hybrid automaton model, the optimal control problem of hybrid system is discussed. Firstly, the description of optimal control is given, then the frame of optimal controller is discussed, finally the complexity of vi optimal control is discussed and analyzed in detail. (3) Switching system is a special kind of hybrid system with certain switching law. The optimal control of switching system is under research, for the discontinuous of boundary of switch systems, the optimal control is not continuous, so that the optimal control problems can抰 be solved by general methods applicable to continuous system. By some transformation, switching system can be shifted to continuous system about certain variables, so that the optimal control can be solved by gradient descendent algorithm which can settle the local optimal control. At last, the gradient of linear system about linear boundary is given. (4) Dynamic programming is an effective algorithm to solve multi-level decision problem. To the autonomous hybrid system with known initial states and fixed run time and unknown final states, the optimal control algorithm is under research, the dynamic programming algorithm based on reachable net is given which can give Out the global optimal control solution and release the computation effectively. (5) Differential dynamic programming can solve the high dimension problem effectively met in dynamic programming. The optimal control of hybrid system with known initial states and run time and unfixed final state is investigated, application of differential dynamic programming under various circumstance such as no cost, constant cost and functional cost of switching is discussed. Algorithm of differential dynamic programming can give out the local optimal control effectively. (6) To the hybrid systems with known initial states, fina...