Single-parameter-learning-based fuzzy fault-tolerant output feedback dynamic surface control of constrained-input nonlinear systems

This paper addresses the problem of adaptive fuzzy fault-tolerant dynamic surface control for a class of constrained-input nonlinear systems. To resolve this problem, the design of an observer-based single-parameter-learning (SPL) control method using output feedback is proposed. The Takagi-Sugeno (T-S) fuzzy system is used to identify and approximate online the uncertain nonlinear dynamics, requiring no knowledge. The barriers that restrict the applications of the traditional backstepping and approximation-based approach, including the explosion of complexity and the dimension curse problems, are circumvented via dynamic surface control and SPL techniques. The merit of the proposed method lies in that only one parameter in the entire control scheme requires online adjustment, regardless of the number of parameters in the T-S fuzzy system that characterizes the fuzzy rules; the calculation burden, in this sense, is reduced to the extent of the minimum value. The truncated adaptation method is used to avoid the chattering and instability caused by constrained input. It is shown with rigorous proof using the Lyapunov and invariant set theorems that all the closed-loop signals are guaranteed semi-globally uniformly ultimately bounded. The output tracking error is adjustable by means of design parameters in an explicit form, and can be adjusted to an arbitrarily small value around zero by appropriately chosen control parameters, even under faulty and constrained actuators. Simulation and comparative results are provided to demonstrate the effectiveness of the proposed control approach.