Adaptive dynamic programming for discrete-time systems with infinite horizon and ∈-error bound in the performance cost

In this paper, we present our work on infinite horizon adaptive dynamic programming problem, which is referred to as isin-adaptive dynamic programming, for discrete-time systems with discount factor 0<gamma<1 in the performance cost. 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.