A New Self-Organizing Fuzzy Cerebellar Model Articulation Controller for Uncertain Nonlinear Systems Using Overlapped Gaussian Membership Functions

Abstract

This article proposes an efficient intelligent control structure for uncertain nonlinear systems. This controller is a new self-organizing fuzzy cerebellar model articulation controller (CMAC), which has a framework that includes a CMAC and which uses sliding mode control. A new mixed Gaussian membership function (GMF) is created using a prior GMF and a present GMF for each layer of the CMAC, which reuses relevant data in the prior GMF to more accurately detect tracking errors. This is more general than the local-feedback of a recurrent unit because inputs can simultaneously stir the present state and the prior state to regulate suitable errors. Using a self-organizing algorithm allows increasing or decreasing the layers so that the structure of the new self-organizing fuzzy CMAC (NSOFC) is constructed automatically. The proposed control system consists of a NSOFC and a compensation controller. The NSOFC is the main tracking controller, and imitates an ideal controller; and the compensator expels the approximation error. A Lyapunov stability function is used to make the system stable, and an adaptive proportional integral method allows online updating of the parameters for efficient control. An inverted double pendulum system and a magnetic levitation system are used to demonstrate that the proposed method gives good tracking performance.