Optimized Backstepping Control Based on Dynamic‐Surface Technique for a Class of Nonlinear Strict‐Feedback Systems Subjected to Actuator Failure

This work develops an optimized backstepping (OB) control by combining the fault‐tolerant mechanism and dynamic surface (DS) technique for a class of nonlinear strict‐feedback systems with actuator failure. OB technique needs to perform the actor‐critic reinforcement learning (RL) at every backstepping step for deriving the optimized virtual and actual controls. However, because of the presence of actuator failures, the RL training will be inevitably affected. To mitigate the effect, an adaptive algorithm is developed to be integrated into the OB control for tolerating the actuator failure. For making the integration smooth, a simplified RL algorithm is deduced from a straightforward positive function derived from the Hamilton‐Jacobi‐Bellman (HJB) equation. Furthermore, since the OB technique requires calculating the derivatives of virtual controls at every backstepping step, it is highly likely to cause the issue of “differential explosion.” To address this problem, DS technique is integrated into the OB control design. Finally, the proposed control method is testified through theory and simulation experiment.