Abstract:
For a class of affine nonlinear systems with actuator faults, this paper proposes a prescribed-time optimal fault-tolerant control strategy based on zero-sum differential games. The methodology constructs state equations with time and space constraint performance through auxiliary functions. Based on these state equations, we establish a differential game model by considering the control signal and bias fault as two game participants. The Hamilton-Jacobi-Isaacs (HJI) equation and Nash-Pontryagin maximin principle are employed to derive the optimal control strategy and boundary values of bias faults, while an adaptive dynamic programming algorithm is implemented to address the curse of dimensionality. The designed optimal fault-tolerant control strategy guarantees prescribed-time stability and optimal performance of the system under actuator faults. Furthermore, the prescribed-time parameter can be flexibly adjusted by users according to specific mission requirements without redesigning gain parameters or considering initial states. Simulation results demonstrate the evolution of system states and control torques under the proposed algorithm, along with comparative analyses of state variations under different initial conditions and prescribed times, which collectively validate the feasibility and effectiveness of the designed methodology.