Zero-Sum Game-Based Hierarchical Sliding-Mode Fault-Tolerant Tracking Control for Interconnected Nonlinear Systems via Adaptive Critic Design

This paper investigates a zero-sum game (ZSG)-based fault-tolerant tracking control problem for a class of interconnected nonlinear systems, in which the faults of each subsystem can affect the other subsystems through couplings. First, a static control policy is developed to transform the fault-tolerant tracking control problem into a ZSG problem of a deduced error system, where the controllers and the faults are regarded as players with opposite interests. Then, based on the sliding mode control technology and the concept of hierarchical design, a novel robust control policy is proposed to regulate the tracking error while minimizing a special cost function. Subsequently, a critic neural network (NN) is trained online to derive the solution of the coupling HJI equation. The critic NN weights are tuned on the basis of the gradient descent approach as well as the historical stored data, such that the persistence of excitation conditions are no longer required. Finally, a simulation example is presented to demonstrate the validity of the proposed control strategy. Note to Practitioners —Since complex modern engineering systems are difficult to be controlled by a single component, the research on adaptive control of interconnected nonlinear systems has become the mainstream trend. In addition, for the practical applications of interconnected systems, fault problems are becoming more common. These faults may make the system difficult to operate normally. Hence, how to guarantee the normal work of the control system when subject to faults has become a hot topic. Furthermore, several engineering applications often take production cost as an important index, and thus it is necessary to design a control strategy that can achieve control objectives with the minimum cost. This paper discusses the optimal fault-tolerant control problem for interconnected nonlinear systems. Meanwhile, a hierarchical sliding-mode control mechanism is designed to improve system robustness.