Sparsity-aware finite abstraction

The abstraction of a continuous-space control system into a dynamical model with finite states and inputs is a key step in automated formal controller synthesis. To date, common software tools have been limited to systems of modest size (typically < 7 dimensions), because the current abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification of the abstraction algorithm, which dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. The modified method recovers the same finite abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speedups from existing benchmarks in the literature, and illustrate the synthesis of a safety controller for a 12-dimensional and the abstraction of a 51-dimensional vehicular traffic network.