Observer-Based Event-Triggered Adaptive Fuzzy Hierarchical Sliding Mode Fault-Tolerant Control for Uncertain Under-Actuated Nonlinear Systems

This paper studies an adaptive fuzzy event-triggered fault-tolerant control (FTC) problem for a category of uncertain under-actuated nonlinear systems with unknown actuator failures based on hierarchical sliding mode surface (HSMS). The under-actuated systems under study contain unknown uncertainty functions, actuator faults, and periodically updated control inputs. First, a fuzzy approximator and a fault observer are used to deal with the unknown functions and actuator failures in the system, respectively, and then, a time-varying bounded function is utilized to transform the control input linearly, making it easy to use in the process of controller design. The robustness and responsiveness of the control system are improved by introducing the HSMS technique in the controller. The HSMS-based active FTC strategy developed in this study enhances the safety and reliability of the controlled system compared to the existing control schemes using HSMS. Meanwhile, as opposed to the fixed-threshold event-triggered control (ETC) scheme, the relative-threshold ETC strategy adopted in this study is able to save communication resources while maintaining a balance between communication cost and control performance. In addition to the repetition amplification caused by the superposition of observation errors, fuzzy approximation errors, and measurement errors, the controller singularity problems are the two main problems caused by the control algorithms. Based on Lyapunov's theory, the proposed scheme ensures that all closed-loop system signals remain bound. Finally, the feasibility and effectiveness of the control strategy are demonstrated through a numerical simulation and a practical example.