Observer-based Adaptive-Fuzzy DSC of Strict-Feedback Nonlinear Delayed Systems with Unknown Control Direction

In this paper, an observer-based adaptive fuzzy back-stepping controller for a class of strict-feedback nonlinear delayed systems with unknown control coefficientis proposed. The system has unknown delayed nonlinear terms and unknown disturbances. The goal is to design an appropriate controller such that the system output tracks the desired trajectory with prescribed bounds while the closed-loop signals remain bounded. An adaptive mechanism is designed such that by using Fuzzy approximators, the unknown functions are approximated via adaptation laws. In addition, an observer is designed such that immeasurable states are estimated. In order to avoid the “explosion of complexity” that exists in traditional back-stepping controllers, the so-called Dynamic Surface Control is used at each steps of the traditional back-stepping approach. Furthermore, Barrier Lyapunov function is employed to consider constraints on the system output. Besides, Nussbaum function is utilized to address the unknown control gain problem. The proposed adaptive controller guarantees that all signals in the closed-loop are semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation results on a delayed nonlinear system with unknown control coefficient confirm the effectiveness of the proposed approach.