Discrete-Time /spl epsilon/-Adaptive Dynamic Programming Algorithm Using Neural Networks

Dynamic programming for discrete time systems is difficult due to the "curse of dimensionality". In this paper, we present our work on dynamic programming for discrete-time system, which is referred as isin-adaptive dynamic programming. A single controller, isin-optimal controller mu_isin*, which is determined from an isin-optimal cost V_isin*, is obtained to approximate the optimal controller. The isin-optimal controller mu_isin* can always control the state to approach the equilibrium state, while the performance cost is close to the biggest lower bound of all performance costs within an error according to isin. An algorithm for finding the isin-optimal controller is developed and numerical experiments are given to illustrate the performance of the algorithm.