Reference
I. Necoara,
T. J. J. van den Boom,
B. De Schutter, and H. Hellendoorn, "Stabilization of max-plus-linear systems
using model predictive control: The unconstrained case,"
Automatica, vol. 44, no. 4, pp. 971-981, Apr. 2008.
Abstract
Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic
systems that can be described by models that are "linear" in the max-plus
algebra. In this paper we derive a solution to a finite-horizon model
predictive control (MPC) problem for MPL systems where the cost is designed to
provide a trade-off between minimizing the due date error and a just-in-time
production. In general, MPC can deal with complex input and states constraints.
However, in this paper we assume that these are not present and it is only
required that the input should be a nondecreasing sequence, i.e. we consider
the "unconstrained" case. Despite the fact that the controlled system is
nonlinear, by employing recent results in max-plus theory we are able to
provide sufficient conditions such that the MPC controller is determined
analytically and moreover the stability in terms of Lyapunov and in terms of
boundedness of the closed-loop system is guaranteed a priori.
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BibTeX
@article{Necvan:06-006,
author = {Necoara, Ion and van den Boom, Ton J. J. and De Schutter, Bart
and Hellendoorn, Hans},
title = {Stabilization of Max-Plus-Linear Systems Using Model Predictive
Control: {The} Unconstrained Case},
journal = {Automatica},
volume = {44},
number = {4},
pages = {971--981},
month = apr,
year = {2008}
}