Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools

Abstract

Polygonal differential inclusion systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. The reachability problem as well as the computation of certain objects of the phase portrait is decidable. In this paper we show how to compute the viability, controllability and invariance kernels, as well as semi-separatrix curves for SPDIs. We also present the tool SPeeDI + , which implements a reachability algorithm and computes phase portraits of SPDIs.

ParaPlan: A Tool for Parallel Reachability Analysis of Planar Polygonal Differential Inclusion Systems

“…In this section we recall the original approach for computing reachable states, which is introduced in [5,3] and based on the characterization of the qualitative behaviours of trajectories.…”

“…In Section 2 we formally describe the class of two-dimensional non-deterministic hybrid systems studied in this paper, namely SPDIs. In Section 3 we recall the original approach for computing reachable states for SPDIs introduced in [5,3] and in Section 4 we present our optimisation of the algorithm and its parallel version. In Section 5 we describe the novel approach for generating random benchmarks.…”