Reference
V. Rostampour, D. Adzkiya, S. Esmaeil Zadeh Soudjani, B. De Schutter, and T.
Keviczky, "Chance-constrained model predictive controller synthesis for
stochastic max-plus linear systems,"
Proceedings of the 2016
IEEE International Conference on Systems, Man, and Cybernetics,
Budapest, Hungary, Oct. 2016.
Abstract
This paper presents a stochastic model predictive control problem for a class
of discrete event systems, namely stochastic max-plus linear systems, which are
of wide practical interest as they appear in many application domains for
timing and synchronization studies. The objective of the control problem is to
minimize a cost function under constraints on states, inputs and outputs of
such a system in a receding horizon fashion. In contrast to the pessimistic
view of the robust approach on uncertainty, the stochastic approach interprets
the constraints probabilistically, allowing for a sufficiently small violation
probability level. In order to address the resulting nonconvex
chance-constrained optimization problem, we present two ideas in this paper.
First, we employ a scenario-based approach to approximate the problem solution,
which optimizes the control inputs over a receding horizon, subject to the
constraint satisfaction under a finite number of scenarios of the uncertain
parameters. Second, we show that this approximate optimization problem is
convex with respect to the decision variables and we provide a-priori
probabilistic guarantees for the desired level of constraint fulfillment. The
proposed scheme improves the results in the literature in two distinct
directions: we do not require any assumption on the underlying probability
distribution of the system parameters; and the scheme is applicable to high
dimensional problems, which makes it suitable for real industrial applications.
The proposed framework is demonstrated on a two-dimensional production system
and it is also applied to a subset of the Dutch railway network in order to
show its scalability and study its limitations.
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BibTeX
@inproceedings{RosAdz:16-030,
author = {Rostampour, Vahab and Adzkiya, Dieky and Esmaeil Zadeh
Soudjani, Sadegh and De Schutter, Bart and Keviczky,
Tam{\'a}s},
title = {Chance-Constrained Model Predictive Controller Synthesis for
Stochastic Max-Plus Linear Systems},
booktitle = {Proceedings of the 2016 IEEE International Conference on
Systems, Man, and Cybernetics},
address = {Budapest, Hungary},
month = oct,
year = {2016}
}