MPC for perturbed max-plus-linear systems

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses (non)linear discrete-time models. Recently we have extended MPC to a class of discrete event systems that can be described by a model that is linear in the (max,+) algebra. Up to now we have only considered the deterministic noise-free case without modeling errors. In this paper we extend our previous results to cases with noise and/or modeling errors. We show that under quite general conditions the resulting optimization problem can be solved very efficiently.

[1]  T. H. Matheiss,et al.  A Survey and Comparison of Methods for Finding All Vertices of Convex Polyhedral Sets , 1980, Math. Oper. Res..

[2]  Lorenz T. Biegler,et al.  Efficient Solution of Dynamic Optimization and NMPC Problems , 2000 .

[3]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[4]  Fag Lin,et al.  Robust and Adaptive Supervisory Control of Discrete Event Systems , 1992, 1992 American Control Conference.

[5]  Jong-Tae Lim,et al.  Fault-tolerant robust supervisor for discrete event systems with model uncertainty and its application to a workcell , 1999, IEEE Trans. Robotics Autom..

[6]  B. Schutter,et al.  Model predictive control for max-plus-linear systems , 2000, ACC.

[7]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[8]  Janette Cardoso,et al.  Possibilistic Petri nets , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[10]  B. De Schutter,et al.  MPC for max-plus-linear systems: closed-loop behavior and tuning , 2001, ACC.

[11]  Bart De Schutter,et al.  Model predictive control for max-plus-linear discrete event systems , 2001, Autom..

[12]  Willi Hock,et al.  Lecture Notes in Economics and Mathematical Systems , 1981 .

[13]  Vijay K. Garg,et al.  Model Uncertainty in Discrete Event Systems , 1995 .

[14]  Eduardo F. Camacho,et al.  Model predictive control in the process industry , 1995 .