Optimal Control of Nonlinear Systems via Predefined-Time Convergent Reinforcement Learning

Abstract

Dear Editor, This letter investigates the optimal control problem for a class of nonlinear systems. The optimal control law is derived from a Hamilton-Jacobi-Bellman (HJB) equation, which is difficult to be solved analytically. To approximate the solution to the HJB equation, a novel predefined-time (PT) convergent reinforcement learning (RL) algorithm is proposed based on a critic neural network (NN). The critic NN employs a novel learning law to update the weight vector. This learning law ensures the PT convergence of the weight vector by introducing a time-dependent adaptive gain and removes the need for the persistent excitation condition via experience replay technology. Furthermore, the PT convergence of the weight vector is theoretically analyzed. Finally, simulations are presented to illustrate the performance of the proposed RL algorithm.