Prescribed performance optimal fault-tolerant control for nonlinear systems with mismatched disturbances via zero-sum differential game

Abstract

This study explores optimal fault-tolerant control with prescribed performance for nonlinear systems affected by mismatched disturbances employing a game-theoretic approach. In the proposed framework, actuator faults and mismatched disturbances are considered together as one player in the game, while the control input acts as the opponent, which adds complexity and interest to the control design. To address this, an innovative fault-tolerant tracking control method is developed by constructing a novel error transformation, adopting a modified performance index with a barrier-type cost, and applying an online critic neural network (NN) algorithm to solve for the Nash equilibrium in the zero-sum differential game. Theoretical analysis confirms that the proposed method ensures system state tracking errors converge to a predetermined precision within a fixed time frame. Furthermore, all closed-loop signals remain uniformly ultimately bounded, validating the control scheme’s optimal performance. Finally, simulation results validate the proposed method’s efficacy and feasibility.