Reference
T. J. J. van den Boom and B. De
Schutter, "Analytic expressions in stochastic max-plus-linear algebra and their
application in model predictive control,"
IEEE Transactions on
Automatic Control, vol. 66, no. 4, pp. 1872-1878, Apr. 2021.
Abstract
The class of max-plus-linear systems can model discrete event systems with
synchronization but no choice. Model mismatch and/or disturbances can be
characterized as stochastic uncertainties. In stochastic max-plus-linear
systems one often needs to compute the expectation of a max-plus-scaling
function or the chance constraint of a max-plus-scaling function. The
algorithms available in literature are either computationally too expensive or
only give an approximation. In this paper we derive an analytic expression for
both the expectation and the chance constraint of a max-plus-scaling function.
Both can be written in the form of a piece-wise polynomial function in the
components of the control variables. The analytic function can be derived
offline and can be evaluated online in a quick and efficient way. We also show
how the expressions can be used in a model predictive control setting and show
the efficiency of the proposed approach with a worked example.
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BibTeX
@article{vanDeS:20-001,
author = {van den Boom, Ton J. J. and De Schutter, Bart},
title = {Analytic Expressions in Stochastic Max-Plus-Linear Algebra and
Their Application in Model Predictive Control},
journal = {IEEE Transactions on Automatic Control},
volume = {66},
number = {4},
pages = {1872--1878},
month = apr,
year = {2021}
}