Adaptive Observer-Based Finite-Time Fault Tolerant Control for Non-Strict Feedback Systems

This paper considers the adaptive finite-time control and observer design method for a class of non-strict feedback systems with unmeasurable states, unknown nonlinear dynamics and actuator faults. In this paper, an observer is proposed to estimate the unmeasurable states in finite-time based on adaptive technique and neural networks, while the actuator faults are not included. Command filter is used to solve the computational explosion and singularity problems caused by the traditional backstepping and non-strict feedback structure, respectively. Since the fault efficiency indicators in real systems are not available, two-layer neural networks are adopted, where the first network is to estimate the unknown nonlinearities of systems and the second one is to estimate fault efficiency indicators and unknown nonlinear terms. The proposed scheme guarantees that states are bounded through stability theorem. Finally, two experiments including a numerical example and a spring-mass-damper system are given to verify the effectiveness of the proposed method.