End-point parametrization and guaranteed stability for a model predictive control scheme

In this paper we consider the closed-loop asymptotic stability of the model predictive control scheme which involves the minimization of a quadratic criterion with a varying weight on the end-point state. In particular, we investigate the stability properties of the (MPC-) controlled system as function of the end-point penalty and provide a useful parametrization of the class of end-point penalties for which stability of the controlled system can be guaranteed. The results are successfully applied for the implementation of an MPC controller of a binary distillation process.

[1]  Carlos E. Garcia,et al.  Internal model control. A unifying review and some new results , 1982 .

[2]  M. Vidyasagar.  Control System Synthesis : A Factorization Approach , 1988 .

[3]  Wook Hyun Kwon,et al.  On stability of constrained receding horizon control with finite terminal weighting matrix , 1997 .

[4]  James B. Rawlings,et al.  Model predictive control with linear models , 1993 .

[5]  M. Gevers,et al.  Fake algebraic Riccati techniques and stability , 1988 .

[6]  Wook Hyun Kwon,et al.  On stabilizing receding horizon controls for linear continuous time-invariant systems , 2000, IEEE Trans. Autom. Control..

[7]  Wook Hyun Kwon,et al.  On stability of constrained receding horizon control with finite terminal weighting matrix , 1997, 1997 European Control Conference (ECC).

[8]  Ian R. Petersen,et al.  Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples☆ , 1985 .

[9]  G. De Nicolao,et al.  On the stability of receding-horizon LQ control with zero-state terminal constraint , 1997, IEEE Trans. Autom. Control..

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  Jobert Ludlage,et al.  On asymptotic stability of a receding horizon control scheme , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  W. Kwon,et al.  A Modified Quadratic Cost Problem and Feedback Stabilization of Linear Discrete Time Systems. , 1977 .

[13]  Wook Hyun Kwon,et al.  Stabilizing receding horizon H∞ controls for linear continuous time-varying systems , 2000, IEEE Trans. Autom. Control..

[14]  Riccardo Scattolini,et al.  On the choice of the horizon in long-range predictive control - Some simple criteria , 1990, Autom..

[15]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[16]  I. Dunn,et al.  Chemical Engineering Dynamics: An Introduction to Modelling and Computer Simulation , 2000 .

[17]  Donal O'Shea,et al.  Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

[18]  Mark J. Damborg,et al.  Heuristically enhanced feedback control of constrained discrete-time linear systems , 1990, at - Automatisierungstechnik.

[19]  J. Rawlings,et al.  The stability of constrained receding horizon control , 1993, IEEE Trans. Autom. Control..

[20]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .