Type-2 fuzzy cerebellar model articulation control system design for MIMO uncertain nonlinear systems
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ORIGINAL ARTICLE
Type‑2 fuzzy cerebellar model articulation control system design for MIMO uncertain nonlinear systems Chih‑Min Lin1 · Ming‑Shu Yang1 Received: 7 August 2016 / Accepted: 6 June 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract This paper aims to propose a more efficient neural network and applies it as an adaptive controller for the multi-input multioutput (MIMO) uncertain nonlinear systems. First, a more efficient fuzzy neural network named as fuzzy cerebellar model articulation controller (CMAC) is introduced, then an adaptive controller is proposed using a novel interval type-2 fuzzy CMAC (T2FCMAC). The T2FCMAC realizes an interval type-2 fuzzy logic system based on the structure of the CMAC. Due to the better ability of handling uncertainties provided by type-2 fuzzy sets, it can solve some complicated problems with outstanding effectiveness than type-1 fuzzy sets. In addition, an intelligent control system is proposed; this control system is comprised of a T2FCMAC and an auxiliary compensation controller. The T2FCMAC is utilized to approximate a perfect controller and the parameters of T2FCMAC are on-line tuned by the derived adaptive laws based on a Lyapunov function. The auxiliary compensation controller is designed to suppress the influence of residual approximation error between the perfect controller and the T2FCMAC. Finally, two MIMO uncertain nonlinear systems, a Chua’s chaotic circuit and a mass-spring-damper mechanical system, are performed to verify the effectiveness of the proposed control scheme. The simulation results confirm that the proposed intelligent adaptive control system can achieve favorable tracking performance with desired robustness. Keywords Adaptive control · Interval type-2 fuzzy system · Cerebellar model articulation controller · Uncertain nonlinear system
1 Introduction Recently, a lot of studies concerning about the design of stabilizing controller for nonlinear systems have been proposed. In some researches, different control methods have been developed from a point of view of dynamic system theory and traditional feedback control algorithm. However, these control schemes can be only applied to nonlinear systems whose dynamic systems are exactly known. This is not sufficient for practical control applications, because it is difficult to establish an exactly mathematical model for a large amount of nonlinear systems. To overcome the problem, the adaptive control methodologies based on Lyapunov * Chih‑Min Lin [email protected] Ming‑Shu Yang [email protected] 1
Department of Electrical Engineering, Yuan Ze University, Taoyuan, Taiwan
stability theorem that incorporate the intelligent systems, such as fuzzy system, neural network, etc., have been grown rapidly for uncertain nonlinear systems [1, 2]. The cerebellar model articulation controller (CMAC) developed by Albus is an artificial neural network inspired by the cerebellum and is classified as a non-fully connected perceptron-like associative memory network with overlap
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