Robust Near-optimal Control for Constrained Nonlinear System via Integral Reinforcement Learning

This paper proposes a robust near-optimal control algorithm for uncertain nonlinear systems with state constraints and input saturation. By incorporating a barrier function and a non-quadratic term, the robust stabilization problem with constraints and uncertainties is converted into an unconstrained optimal control problem of the nominal system, which requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation. The proposed integral reinforcement learning (IRL)-based method can obtain the approximate solution of the HJB equation without requiring any knowledge of system drift dynamics. An online gain-adjustable update law of the actor-critic architecture is developed to relax the persistence of excitation (PE) condition and ensure the closed-loop system stability throughout learning. The uniform ultimate boundedness of the closed-loop system is verified using Lyapunov’s direct method. Simulation results demonstrate the effectiveness and feasibility of the proposed method.