Sparsity-Sensitive Finite Abstraction
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 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.
Cite
@article{arxiv.1704.03951,
title = {Sparsity-Sensitive Finite Abstraction},
author = {Felix Gruber and Eric S. Kim and Murat Arcak},
journal= {arXiv preprint arXiv:1704.03951},
year = {2018}
}