Nonlinear system modeling and robust predictive control based on RBF-ARX model

Authors:
Hui Peng;Zi-Jiang Yang;Weihua Gui;Min Wu;Hideo Shioya;Kazushi Nakano
Affiliations:
School of Information Science & Engineering, Central South University, Changsha, Hunan 410083, China;Department of Electrical and Electronic Systems Engineering, Kyushu University, Fukuoka 812-8581, Japan;School of Information Science & Engineering, Central South University, Changsha, Hunan 410083, China;School of Information Science & Engineering, Central South University, Changsha, Hunan 410083, China;Bailey Japan Co. Ltd., 511 Baraki, Nirayama-cho, Tagata-gun, Shizuoka 410-2193, Japan;Department of Electronic Engineering, the University of Electro-Communications, 1-5-1 Chofu-ga-oka, Chofu, Tokyo 182-8585, Japan
Venue:
Engineering Applications of Artificial Intelligence
Year:
2007

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Abstract

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min-max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NO"x decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.