A modified function-link fuzzy cerebellar model articulation controller using a PI-type learning algorithm for nonlinear system synchronization and control

Abstract This paper aims to propose a novel modified fuzzy cerebellar model articulation controller (CMAC) combined with a function-link network for the synchronization of nonlinear chaotic systems and control of an inverted pendulum in the presence of uncertainties, external disturbance, and different initial conditions. The proposed method overlaps the previous state and the current state of Gaussian basis functions (GBFs) on each layer to make a combination between two states. This makes the inputs be able to simultaneously stir the current state and previous state to adjust the appropriate error values so that the modified function-link fuzzy CMAC (FLMFC) can easily learn parameters, improve the computational efficiency and predict the next state of the inputs. The proposed control system combines an FLMFC with the sliding mode control; therefore the input space element of FLMFC can be simplified. A function-link network is embedded in the FLMFC to give a more accurate approximation of the weights. A PI-type learning method is used to online tune the parameters for the connective weights of the proposed FLMFC. The control system consists of an FLMFC and a compensation controller. A Lyapunov stability theorem is applied to find the adaptation laws of the proposed controller and to guarantee the system's stability. Simulation studies for the synchronization of chaotic systems and control of inverted pendulum show that favorable tracking performance can be achieved by using the proposed control system.