Researches On Optimal Tracking Control For A Class Of Discrete-Time Nonlinear Systems With Time Delays Based On Heuristic Dynamic Programming

Time delay is an ubiquitous phenomenon, chemical process systems、transmission systems、power systems are typical of the time delay system. Time delays could result in the effectiveness of the controller reduced, the worst case may lead to deterioration of system performance, and even system instability. So the study of delay systems without interruption, especially in the field of control, time delay problem has been the focus of attention in the field.Adaptive Dynamic Programming (ADP) is an optimization algorithm, which based on dynamic programming、reinforcement learning and back-propagation. The core idea ofthe adaptive dynamic programming is to approximate the performance function of the system to get the optimal control, the algorithm avoids the "curse of dimensionality" of dynamic programming, it is very appropriately used in the noisy、non-linear and non-stationary environments, and the algorithm is also considered to be a very effective method to solve the optimal control problem. In recent years, the algorithm gets close attention of many scholars.In this paper, definition of delay systems and the basic principles of the Heuristic Dynamic Programming (HDP) are firstly described, and then focus on the study of the optimal tracking control problem of time delay system based on the ADP algorithm. On the one hand, for a class of nonlinear discrete-time systems with time delay, by defining the error function, conversion of system and using a new type of performance index function for the tracking problem, then the optimal tracking control problem is transformed to the optimal regulation problem, and then use the HDP algorithm to solve the optimal tracking control problem; On the other hand, based on the optimal tracking control without time delay, by introducing the time delay function, the time-varying optimal tracking problem of the nonlinear discrete systems with state delay and control delay is solved by using the HDP algorithm. In order to verify the validity of the algorithm for the no-delay systems and delay systems, the fixed-point tracking and time-varying tracking simulation examples are given. Finally, the studies in this paper is summarized and the next step of the study is pointed out.