Global Robust Optimal Sliding Mode Control for a Class of Affine Nonlinear Systems with Uncertainties Based on SDRE

Integrating the sliding mode control (SMC) theory with state-dependent Riccati equation (SDRE), a new design method of global robust optimal sliding mode control for a class of affine nonlinear systems with uncertainties is studied in this paper. First, by using the SDRE approach, an optimal control law for nonlinear systems without uncertainties is obtained. Then the sliding mode control theory is used to robustify the optimal control system, which is affected by the parameter variations or extraneous disturbances. As a result, the system is global robust to uncertainties. So the global robust optimal sliding mode control base on SDRE is realized. Finally, the optimal performance and robustness to system uncertainty of the proposed approach are demonstrated successfully by a simulation example.