Reinforcement learning-based robust optimal tracking control for disturbed nonlinear systems

This paper concludes a robust optimal tracking control law for a class of nonlinear systems. A characteristic of this paper is that the designed controller can guarantee both robustness and optimality under nonlinearity and mismatched disturbances. Optimal controllers for nonlinear systems are difficult to obtain, hence a reinforcement learning method is adopted with two neural networks (NNs) approximating the cost function and optimal controller, respectively. We designed weight update laws for critic NN and actor NN based on gradient descent and stability, respectively. In addition, matched and mismatched disturbances are estimated by fixed-time disturbance observers and an artful transformation based on backstepping method is employed to convert the system into a filtered error nonlinear system. Through a rigorous analysis using the Lyapunov method, we demonstrate states and estimation errors remain uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified through two illustrative examples.