Indirect adaptive fuzzy control of non-linear systems using fuzzy supervisory term

This paper focuses on the indirect adaptive fuzzy control of Single Input Single Output (SISO) non-linear systems with unknown linearities. The proposed adaptive fuzzy controller is based on feedback linearisation. Its parameters are updated online according to some adaptive laws such as tracking error-based method, composite tracking and modelling error-based approach as well as filtered composite tracking and modelling error-based approach. However, the approximation error introduced into feedback loop increases the difficulty to guarantee the stability of the closed-loop control system. To solve this problem a supervisory term should be added to the control law. In this paper, a fuzzy supervisory control is proposed to overcome the problem of chattering phenomena introduced by the classical supervisory term. Theoretical and simulation results prove the effectiveness of the proposed approaches. Faster and improved tracking is obtained by using second and third aforementioned adaptive laws combined with fuzzy supervisory control.