Sliding Mode-Based Approximate-Optimal Control of Unknown Second-Order Nonaffine Systems Subject to Input Saturation

This paper presents a new method to achieve approximate-optimal control of second-order nonaffine nonlinear systems with unknown dynamics, external disturbance, and input saturation by integrating a pre-compensator, the adaptive dynamic programming (ADP) technique, and a disturbance compensator. The pre-compensator transforms the nonaffine system into an affine-like one and integrates a saturation condition into the augmented system to address input saturation. A new quadratic cost function based on sliding mode (SM) is proposed for the augmented system to simplify the cost function's dimensionality, which enhances the efficiency of the algorithm. A compensation term is further proposed to counteract the unknown bounded disturbances. We will show that, the designed robust sliding mode-based ADP (SMADP) guarantees the asymptotic stability of the closed-loop system and, by utilizing neural networks (NNs) to approximate the optimal value of the cost function, the resulting NN-based SMADP algorithm can also guarantees the uniform ultimate boundedness of the trajectory of the closed-loop system. The simulation results validate the effectiveness of our SM-based robust ADP control method.