A Contractive Sliding- mode MPC Algorithm for Nonlinear Discrete- time Systems

This paper investigates a sliding-mode model predictive control (MPC) algorithm with auxiliary contractive sliding vector constraint for constrained nonlinear discrete-time systems. By adding contractive constraint into the optimization problem in regular sliding-mode MPC algorithm, the value of the sliding vector is decreased to zero asymptotically, which means that the system state is driven into a vicinity of sliding surface with a certain width. Then, the system state moves along the sliding surface to the equilibrium point within the vicinity. By applying the proposed algorithm, the stability of the closed-loop system is guaranteed. A numerical example of a continuous stirred tank reactor (CSTR) system is given to verify the feasibility and effectiveness of the proposed method.

[1]  Tor Arne Johansen,et al.  Approximate explicit receding horizon control of constrained nonlinear systems , 2004, Autom..

[2]  Manfred Morari,et al.  Contractive model predictive control for constrained nonlinear systems , 2000, IEEE Trans. Autom. Control..

[3]  Bijnan Bandyopadhyay,et al.  Sliding Mode Control Using Novel Sliding Surfaces , 2009 .

[4]  F. Allgöwer,et al.  Nonlinear Model Predictive Control: From Theory to Application , 2004 .

[5]  Run Pei,et al.  Sliding mode model predictive control with terminal constraints , 2000, Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No.00EX393).

[6]  Weibing Gao,et al.  Variable structure control of nonlinear systems: a new approach , 1993, IEEE Trans. Ind. Electron..

[7]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[8]  封锡盛,et al.  State Feedback Sliding Mode Control without Chattering by Constructing Hurwitz Matrix for AUV Movement , 2011 .

[9]  Frank Allgöwer,et al.  State and Output Feedback Nonlinear Model Predictive Control: An Overview , 2003, Eur. J. Control.

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

[11]  Hongye Su,et al.  Variable structure control with sliding mode prediction for discrete-time nonlinear systems , 2006 .

[12]  Rafael Fierro,et al.  Stabilization of Nonholonomic Robot Formations: A First-state Contractive Model Predictive Control Approach , 2009, J. Comput. Inf. Technol..

[13]  Oscar Camacho,et al.  Development of a GPC-based sliding mode controller. , 2002, ISA transactions.

[14]  Michael A. Henson,et al.  Nonlinear model predictive control: current status and future directions , 1998 .

[15]  H. ChenT,et al.  A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability * , 1998 .

[16]  Wen-Hua Chen,et al.  Model predictive control of nonlinear systems: Stability region and feasible initial control , 2007, Int. J. Autom. Comput..

[17]  O. Kaynak,et al.  On the stability of discrete-time sliding mode control systems , 1987 .

[18]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[19]  Riccardo Scattolini,et al.  A stabilizing model-based predictive control algorithm for nonlinear systems , 2001, Autom..

[20]  Ilya V. Kolmanovsky,et al.  A stable block model predictive control with variable implementation horizon , 2005, Proceedings of the 2005, American Control Conference, 2005..

[21]  E. Gilbert,et al.  Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations , 1988 .