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

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.

[1]  Yukihiro Toyoda,et al.  A nonlinear exponential ARX model-based multivariable generalized predictive control strategy for thermal power plants , 2002, IEEE Trans. Control. Syst. Technol..

[2]  Tohru Ozaki,et al.  Modeling and control of nonlinear nitrogen oxide decomposition process , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  Mahdi Mahfouf,et al.  Non-linear generalized predictive control (NLGPC) applied to muscle relaxant anaesthesia , 1998 .

[4]  Yaman Arkun,et al.  Scheduling quasi-min-max model predictive control algorithm for nonlinear systems , 2001, 2001 European Control Conference (ECC).

[5]  Makoto Suzuki,et al.  Improvement of de-NOx device control performance using a software sensor , 1997 .

[6]  Kazushi Nakano,et al.  RBF-ARX model based nonlinear system modeling and predictive control with application to a NOx decomposition process , 2004 .

[7]  Makoto Suzuki,et al.  Improvement of De-NOx Device Control Performance Using Software Sensor , 1997 .

[8]  H. Bloemen,et al.  Model-based predictive control for Hammerstein?Wiener systems , 2001 .

[9]  M. Mokhtari,et al.  Adaptive Predictive Control of a Class of Nonlinear Systems: A Case Study , 1995 .

[10]  Yukihiro Toyoda,et al.  A parameter optimization method for radial basis function type models , 2003, IEEE Trans. Neural Networks.

[11]  Manfred Morari,et al.  An improved approach for constrained robust model predictive control , 2002, Autom..

[12]  Alfredo C. Desages,et al.  Approximate models for nonlinear process control , 1996 .

[13]  Frank Allgöwer,et al.  Nonlinear Model Predictive Control , 2007 .

[14]  Janko Petrovčič,et al.  NOX selective catalytic reduction control based on simple models , 2001 .

[15]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[16]  K. Nakano,et al.  Stability analysis of the RBF-ARX model based nonlinear predictive control , 2003, 2003 European Control Conference (ECC).

[17]  E. Swidenbank,et al.  A Local Model Networks Based Multivariable Long-Range Predictive Control Strategy for Thermal Power Plants , 1998, Autom..

[18]  M. Kothare,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.