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In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults. First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network (NN) is pre-trained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control, respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle. The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and supe-riority of the developed fault-tolerant tracking control scheme.
Wang et al. (Wed,) studied this question.