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arXiv · 1704.03951

Sparsity-Sensitive Finite Abstraction

Felix Gruber·Eric S. Kim·Murat Arcak
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Abstract

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network.

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BibTeXRIS

Felix Gruber, Eric S. Kim, Murat Arcak. 2017-04-12. Sparsity-Sensitive Finite Abstraction. https://doi.org/10.1109/cdc.2017.8263995

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