Alexander Weber, Matthias Rungger, Gunther Reissig.

Optimized State Space Grids for Abstractions.

IEEE Trans. Automat. Control, vol. 62, no. 11, Nov 2017,
pp. 5816-5821.

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

The practical impact of abstraction-based controller synthesis methods
is currently limited by the immense computational effort for obtaining
abstractions. In this note we focus on a recently proposed method to
compute abstractions whose state space is a cover of the state space
of the plant by congruent hyper-intervals. The problem of how to
choose the size of the hyper-intervals so as to obtain computable and
useful abstractions is unsolved. This note provides a twofold
contribution towards a solution. Firstly, we present a functional to
predict the computational effort for the abstraction to be
computed. Secondly, we propose a method for choosing the aspect ratio
of the hyper-intervals when their volume is fixed. More precisely, we
propose to choose the aspect ratio so as to minimize a predicted
number of transitions of the abstraction to be computed, in order to
reduce the computational effort. To this end, we derive a functional
to predict the number of transitions in dependence of the aspect
ratio. The functional is to be minimized subject to suitable
constraints. We characterize the unique solvability of the respective
optimization problem and prove that it transforms, under appropriate
assumptions, into an equivalent convex problem with strictly convex
objective. The latter problem can then be globally solved using
standard numerical methods. We demonstrate our approach on an example.

**BibTeX entry:**

@article{WeberRunggerReissig17,
AUTHOR = {Alexander Weber and Matthias Rungger and Reissig, Gunther},
TITLE = {Optimized State Space Grids for Abstractions},
year = 2017,
journal = {IEEE Trans. Automat. Control},
volume = {62},
number = 11,
pages = {5816-5821},
month = nov,
doi ={10.1109/TAC.2016.2642794}
}

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