Approximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faults

In this paper, the guaranteed cost fault-tolerant control problem for unknown multi-input continuous nonlinear systems with loss of actuator effectiveness faults is investigated using the adaptive dynamic programming algorithm. Initially, by modifying the cost function to account for actuator faults, the problem is transformed into an optimal control problem of the nominal system. Subsequently, by using an existing policy iteration (PI) algorithm to solve the corresponding optimal control problem, a guaranteed cost controller is constructed approximately. Furthermore, a rigorous proof is given to show the convergence of the aforementioned PI algorithm while taking the neural network approximation errors into consideration. Finally, simulation examples are provided to show the effectiveness of the proposed approach.