Adaptive critic design for safety-optimal FTC of unknown nonlinear systems with asymmetric constrained-input

Safe fault tolerant control is one of the key technologies to improve the reliability of dynamic complex nonlinear systems with limited inputs, which is hard to solve and definitely a great challenge to tackle. Thus the paper presents a novel safety-optimal FTC (Fault Tolerant Control) approach for a category of completely unknown nonlinear systems incorporating actuator fault and asymmetric constrained-input, which can guarantee the system's operation within a safe range while showcasing optimal performance. Firstly, a CBF (Control Barrier Function) is incorporated into the cost function to penalize unsafe behaviors, and then we translate the intractable safety-optimal FTC problem into a differential ZSG (Zero-Sum Game) problem by defining the control input and the actuator fault as two opposing sides. Secondly, a neural-network-based identifier is employed to reconstruct system dynamics using system data, and the resolution of handling asymmetric constrained-input with the introduced non-quadratic cost function is achieved through the design of an adaptive critic scheme, aiming to reduce computational expenses accordingly. Finally, through the theoretical stability analysis, it is demonstrated that all signals in the closed-loop system are consistently UUB (Uniformly Ultimately Bounded). Furthermore, the proposed method's effectiveness is also verified in the simulation experiments conducted on a model of a single-link robotic arm system with actuator failure. The result shows that the algorithm can fulfill the safety-optimal demand of fault tolerant control in fault system with asymmetric constrained-input.