Gunther Reißig.

Computation of discrete abstractions of arbitrary memory span for
nonlinear sampled systems.

Proc. 12th Intl. Conf. Hybrid Systems: Computation and Control
(HSCC), San Francisco, U.S.A., April 13-15, 2009,
vol. 5469 of Lect. N. Computer Science, pp. 306-320,
R. Majumdar and P. Tabuada, eds.,
Springer, 2009.

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**Abstract:**

In this paper, we present a new method for computing discrete
abstractions of arbitrary memory span for nonlinear sampled systems
with quantized output. In our method, abstractions are represented by
collections of conservative approximations of reachable sets by
polyhedra, which in turn are represented by collections of
half-spaces. Important features of our approach are that half-spaces
are shared among polyhedra, and that the determination of each
half-space requires the solution of a single initial value problem in
an ordinary differential equation over a single sampling interval
only. Apart from these numerical integrations, the only nontrivial
operation to be performed repeatedly is to decide whether a given
polyhedron is empty. In particular, in contrast to previous
approaches, there are no intermediate bloating steps, and convex hulls
are never computed. Our method heavily relies on convexity of
reachable sets and applies to any sufficiently smooth system if either
the sampling period, or the system of level sets of the quantizer can
be chosen freely. In particular, it is not required that the system
to be abstracted have any stability properties.

**BibTeX entry:**

@InProceedings{Reissig11C,
author = {Gunther Rei{\ss}ig},
title = {Computation of discrete abstractions of arbitrary memory span for nonlinear sampled systems},
booktitle = {Proc. 12th Intl. Conf. Hybrid Systems: Computation and Control (HSCC), San Francisco, U.S.A., April 13-15, 2009},
pages = {306-320},
year = 2009,
editor = {R. Majumdar and P. Tabuada},
volume = 5469,
publisher = {Springer},
series = {Lect. Notes Computer Science},
doi = {10.1007/978-3-642-00602-9_22}
}

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