Towards Computing Phase Portraits of Polygonal Differential Inclusions

SPeeDI — A Verification Tool for Polygonal Hybrid Systems

“…We plan to extend its functionality beyond reachability verification. In particular, we are currently working on the implementation of the algorithm developed in [10] for constructing the phase portrait of an SPDI which is composed of viability and controllability kernels.…”

A Compositional Algorithm for Parallel Model Checking of Polygonal Hybrid Systems

“…We recall the definition of controllability and viability kernels of an SPDI and we show how to obtain such kernels -proofs are omitted and for further details, refer to [ASY02]. In the following, given σ a cyclic signature, we define K σ as follows:…”

Computation and Visualisation of Phase Portraits for Model Checking SPDIs

“…+ implements the algorithms published in [7,8] based on the analysis of qualitative behaviours generated by a discrete dynamical system characterised by positive affine Poincaré maps. Currently there are no other tools specifically for SPDI analysis.…”

“…We call the set of all such objects the phase portrait of the system. Defining and constructing phase portraits of hybrid systems has been directly addressed for SPDIs in [7,8]. In this paper we present a tool implementing the generation of phase portraits for SPDIs following the latter papers, and we show how these can be used to optimise the reachability analysis, in some cases even giving an immediate answer, as exposed in [9].…”

“…The information gathered for computing reachability turns out to be useful for computing certain phase portrait objects of SPDIs. Given a cycle on a SPDI, we can speak about a number of kernels pertaining to that cycle [7,8]. The viability kernel is the largest set of points in the cycle which may loop forever within the cycle.…”