Robust approximate optimal sliding mode control for a class of affine nonlinear systems with uncertainties

Integrating the optimal control theory with sliding mode control theory, a global robust optimal sliding mode controller (GROSMC) for a class of affine nonlinear systems with uncertainties is proposed. The optimal control problem for nonlinear systems often leads to a nonlinear HJB (Hamilton Jacobi Bellman) equation which is difficult to solve. Firstly, an approximate optimal control law for nonlinear system without uncertainties is obtained with θ - D method. The method is carried out by solving the HJB equation approximately by adding perturbations to the cost function. Secondly, the sliding mode control theory is used to robustify the designed optimal controller, thus the dynamic system exhibits global robustness to the uncertainties. So a global robust optimal sliding mode controller is realized. Finally, the proposed approach is applied to a ball-beam system. The simulation results show the effectiveness and superiority of the proposed algorithm.