Reference
A. Bemporad,
W. P. M. H.
Heemels, and B. De Schutter, "On hybrid systems and closed-loop MPC systems,"
IEEE Transactions on Automatic Control, vol. 47, no. 5,
pp. 863-869, May 2002.
Abstract
The following five classes of hybrid systems were recently proven to be
equivalent: linear complementarity, extended linear complementarity, mixed
logical dynamical, piecewise affine, and max-min-plus-scaling systems. Some of
the equivalences were obtained under additional assumptions, such as
boundedness of certain 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, fulfilling linear constraints on input and state variables, and
utilizing a quadratic cost criterion, we provide a simple and direct proof that
the closed-loop system is a subclass of any of the former five classes of
hybrid systems. This result is of extreme importance as it opens up the use of
tools developed for the mentioned hybrid model classes, such as (robust)
stability and safety analysis tools, to study closed-loop properties of MPC.
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BibTeX
@article{BemHee:02-003,
author = {Bemporad, Alberto and Heemels, W. P. M. H. and De Schutter,
Bart},
title = {On Hybrid Systems and Closed-Loop {MPC} Systems},
journal = {IEEE Transactions on Automatic Control},
volume = {47},
number = {5},
pages = {863--869},
month = may,
year = {2002}
}