Reference
A. Bemporad,
W. P. M. H.
Heemels, and B. De Schutter, "On hybrid systems and closed-loop MPC systems,"
Proceedings of the 40th IEEE Conference on Decision and
Control, Orlando, Florida, pp. 1645-1650, Dec. 2001.
Abstract
The following five classes of hybrid systems were recently proved to be
equivalent: linear complementarity (LC) systems, extended linear
complementarity (ELC) systems, mixed logical dynamical (MLD) systems, piecewise
affine (PWA) systems, and max-min-plus-scaling (MMPS) systems. Some of the
equivalences were obtained under additional assumptions, such as boundedness of
system variables. In this paper, for linear or hybrid plants in closed-loop
with a model predictive control (MPC) controller based on a linear model and
fulfilling linear constraints on input and state variables, we provide a simple
and direct proof that the closed-loop system (cl-MPC) is a subclass of any of
the former five classes of hybrid systems. This result opens the use of tools
developed for hybrid systems (such as stability, robust stability, and safety
analysis tools) to study closed-loop properties of MPC.
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BibTeX
@inproceedings{BemHee:01-02,
author = {Bemporad, Alberto and Heemels, W. P. M. H. and De Schutter,
Bart},
title = {On Hybrid Systems and Closed-Loop {MPC} Systems},
booktitle = {Proceedings of the 40th IEEE Conference on Decision and
Control},
address = {Orlando, Florida},
pages = {1645--1650},
month = dec,
year = {2001}
}