adaptive fuzzy controller

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.

Nowadays according to the rapid growth of the fractional order calculus, this field has converted to a beloved context for researchers. Also, there have been introduced various control algorithms with the fractional order approach. On the other hand, it has been proved that fuzzy systems are capable of controlling uncertain system with disturbance if they are well equipped with the expert knowledge. However, when there is not enough information to build fuzzy system or the expert knowledge cannot be properly transformed to the fuzzy inference part, a fuzzy system is not a universal approximation and cannot be applied. For these reasons, this paper proposes a direct adaptive fuzzy system with compensation to control a certain class of fractional order nonlinear systems with unknown nonlinearities. The stability criterion in fractional order definition is studied and based on a Lyapunov function candidate. Using the Lyapunov theorem ensures global Mittag-Leffler stability of the closed loop system. Free parameters are adjusted online and kept limited by the fractional order adaptation law, which is kept limited with a projection algorithm. In addition, according to the proposed method, the plant, which is little known, can be controlled effectively no matter whether the membership functions are suitable or not. Two numerical simulations show validity and effectiveness of the introduced control strategy for fractional order nonlinear models that perturbed by disturbance and uncertainty.