Fuzzy adaptive fault-tolerant tracking algorithm based on event-triggered for stochastic nonlinear systems

The focus of this article is to develop a novel adaptive fuzzy fault-tolerant algorithm for stochastic nonlinear systems with unmodeled dynamics, sensor and actuator faults. During the design process of the algorithm, two main difficulties are encountered: 1)The presence of actuator faults and multiple sensor faults in the system; 2)The presence of stochastic noise and uncertain nonlinear terms in the system. To handle these problems, multiple adaptive laws are introduced to compensate for the effects of sensor and actuator faults. Furthermore, the unknown nonlinear terms are estimated effectively by the universal approximation capability of fuzzy logic systems. At the same time, to save the communication resources, event-triggered mechanism and quantized control scheme are introduced in the design of the controller to avoid Zeno behavior effectively. On this basis, the designed fault-tolerant controller not only ensures that all signals within the closed-loop system remain bounded in the finite time but also guarantees that the tracking error converges to a small neighborhood near the origin. Ultimately, the validity of the proposed algorithm is verified through its application to two examples, one of which is a classic mass–spring–damper system that may be influenced by factors including friction, vibration, bias errors, and gain variations.