Reference
T. J. J. van den Boom and B. De
Schutter, "Modeling and control of switching max-plus-linear systems with
random and deterministic switching,"
Discrete Event Dynamic
Systems: Theory and Applications, vol. 22, no. 3, pp. 293-332, Sept.
2012.
Abstract
Switching max-plus-linear (SMPL) systems are discrete-event systems that can
switch between different modes of operation. In each mode the system is
described by a max-plus-linear state equation and a max-plus-linear output
equation, with different system matrices for each mode. The switching may
depend on the inputs and the states, or it may be a stochastic process.
In this paper two equivalent descriptions for switching max-plus-linear systems
will be discussed. We will also show that a switching max-plus-linear system
can be written as a piecewise affine system or as a constrained
max-min-plus-scaling system. The last translation can be established under
(rather mild) additional assumptions on the boundedness of the states and the
inputs.
We also develop a stabilizing model predictive controller for SMPL systems with
deterministic and/or stochastic switching. In general, the optimization in the
model predictive control approach then boils down to a nonlinear nonconvex
optimization problem, where the cost criterion is piecewise polynomial on
polyhedral sets and the inequality constraints are linear. However, in the case
of stochastic switching that depends on the previous mode only, the resulting
optimization problem can be solved using linear programming algorithms.
Publisher page
Downloads
BibTeX
@article{vanDeS:11-042,
author = {van den Boom, Ton J. J. and De Schutter, Bart},
title = {Modeling and Control of Switching Max-Plus-Linear Systems with
Random and Deterministic Switching},
journal = {Discrete Event Dynamic Systems: Theory and Applications},
volume = {22},
number = {3},
pages = {293--332},
month = sep,
year = {2012}
}