Reference
D. Adzkiya, B. De Schutter, and A. Abate, "Finite abstractions of nonautonomous
max-plus-linear systems,"
Proceedings of the 2013 American
Control Conference, Washington, DC, pp. 4393-4398, June 2013.
Abstract
This work puts forward a technique to generate finite abstractions of
nonautonomous Max-Plus-Linear (MPL) models, a known class of discrete-event
systems characterizing the timing related to event counters. Nonautonomous
models embed an external input (namely a nondeterministic choice, regarded as
an exogenous control signal) in the dynamics. Abstractions are characterized as
finite-state Labeled Transition Systems (LTS). LTS are obtained first by
partitioning the state space of the MPL model and by associating states of the
LTS to the introduced partitions, then by defining relations among the states
of the LTS, corresponding to the dynamical (nonautonomous) transitions between
the MPL state partitions, and finally by labeling the LTS edges according to
the one-step timing properties related to the events of the original MPL model.
In order to establish formal equivalences, the finite LTS abstraction is proven
either to simulate or to bisimulate the original MPL model. The computational
performance of the abstraction procedure is tested on a numerical benchmark.
The approach enables the study of properties of the original MPL model by
verifying equivalent specifications over the finite LTS abstraction.
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BibTeX
@inproceedings{AdzDeS:13-007,
author = {Adzkiya, Dieky and De Schutter, Bart and Abate, Alessandro},
title = {Finite Abstractions of Nonautonomous Max-Plus-Linear Systems},
booktitle = {Proceedings of the 2013 American Control Conference},
address = {Washington, DC},
pages = {4393--4398},
month = jun,
year = {2013}
}