Matthias Rungger,
Alexander Weber,
Gunther Reissig.

State Space Grids for Low Complexity Abstractions.

Proc. 54nd IEEE Conf. Decision and Control (CDC),
Osaka, Japan,
15-18 Dec. 2015, pp. 6139-6146.

Full text.
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Full text.
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**Abstract:**

We consider an automated, algorithmic controller synthesis framework
for perturbed nonlinear control systems to enforce complex
specifications, in which an auxiliary transition system, also known as
abstraction or symbolic model, is used as a finite
substitute of the original control system in the controller design
process. We specifically focus on reducing the computational effort to
obtain abstractions, which is the most expensive step in the
approach. To this end, we derive a functional to estimate the size of
the abstraction, specifically, the number of transitions, and prove
that after a suitable transformation the functional becomes strongly
convex. Thus, the minimization of the estimated size of the
abstraction is an unconstrained strongly convex optimization problem,
which is straightforward to solve using standard methods. This permits
us to use this functional as a heuristic to determine certain grid
parameters for the construction of abstractions. We illustrate the
benefits of the newly developed heuristic for two numerical examples.

**BibTeX entry:**

@InProceedings{RunggerWeberReissig15,
author = {Matthias Rungger and Alexander Weber and Gunther Reissig},
title = {State Space Grids for Low Complexity Abstractions},
booktitle = {Proc. IEEE Conf. Decision and Control (CDC), Osaka, Japan, 15-18 } # dec # { 2015},
pages = {6139-6146},
year = {2015},
address = {New York},
publisher = {IEEE},
doi = {10.1109/CDC.2015.7403185}
}

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