Predictive control of constrained nonlinear systems via LPV linear embeddings

This paper analyzes the applicability of convex MPC schemes, synthesized for LPV polytopic systems, to nonlinear plants. The nonlinear systems under consideration are those whose trajectories can be embedded within those of a polytopic LPV discrete-time system. It is postulated that the latter belongs to a polytopic family of linear systems, each member of which is parameterized by the value that a parameter vector assumes in the unit simplex. Such a parameter can be measured on-line and exploited for feedback while a bound on its rate of change is known and exploited for predictions. Different customizations and improvements of a recently introduced MPC scheme for LPV systems are presented and contrasted in terms of their numerical burdens and control performance. The proposed predictive controllers are proved to quadratically stabilize LPV polytopic systems, as well as any other embedded non-linear system, in the presence of input and state constraints. Copyright © 2003 John Wiley & Sons, Ltd.

[1]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

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

[3]  Yaman Arkun,et al.  Quasi-Min-Max MPC algorithms for LPV systems , 2000, Autom..

[4]  Edoardo Mosca,et al.  Constrained predictive control of nonlinear plants via polytopic linear system embedding , 2000 .

[5]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[6]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[7]  Ruey-Wen Liu Convergent systems , 1968 .

[8]  Alessandro Casavola,et al.  A feedback min-max MPC algorithm for LPV systems subject to bounded rates of change of parameters , 2002, IEEE Trans. Autom. Control..

[9]  B. Anderson,et al.  Detectability and Stabilizability of Time-Varying Discrete-Time Linear Systems , 1981 .

[10]  Edoardo Mosca,et al.  Robust command governors for constrained linear systems , 2000, IEEE Trans. Autom. Control..

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

[12]  Stephen J. Wright,et al.  Nonlinear Predictive Control and Moving Horizon Estimation — An Introductory Overview , 1999 .

[13]  Edoardo Mosca,et al.  Min-max predictive control strategies for input-saturated polytopic uncertain systems , 2000, Autom..

[14]  P. Peres,et al.  On a convex parameter space method for linear control design of uncertain systems , 1991 .

[15]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[16]  L. El Ghaoui,et al.  Robust gain-scheduled control of a class of nonlinear parameter-dependent systems: application to an uncertain inverted pendulum , 1996, Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro.