Reinforcement learning-based online adaptive controller design for a class of unknown nonlinear discrete-time systems with time delays

This paper is concerned with online adaptive control strategy for a class of unknown nonlinear discrete-time systems with time delays. The main objective is to establish an online adaptive control strategy based on reinforcement learning (RL) algorithm, so that the nonquadratic performance index can be minimized and the closed-loop system with time delays is stable. In order to simplify the control systems with time delays, a time delay function is designed to eliminate the term of control delays. Then, the online adaptive control algorithm via RL is presented to approach the reasonable control law and optimizes the long-term performance function. On the basis of the Lyapunov theory, it is proved that the design of online adaptive controller is effective and all the signals of control system are ultimately uniformly bounded. The simulation results indicate the validity and feasibility of the proposed adaptive control strategy.