Relaxing Goodness Is Still Good

Abstract

Abstract. Polygonal hybrid systems (SPDIs) are planar hybrid systems, whose dynamics are defined in terms of constant differential inclusions, one for each of a number of polygonal regions partitioning the plane. The reachability problem for SPDIs is known to be decidable, but depends on the goodness assumptionwhich states that the dynamics do not allow a trajectory to both enter and leave a region through the same edge. In this paper we extend the decidability result to generalised SPDIs (GSPDI), SPDIs not satisfying the goodness property, and give an algorithmic solution to decide reachability of such systems.

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

“…Figure 3: Red dots denote the output edges for the upper region, and blue dots denote the output edges for the lower region. The oriented angles between edges (6-11) and (2-5) for the upper region, and between edges (10-11) and (12)(13)(14) for the lower region, are positive.…”

“…The decidability result for SPDIs has also been extended to generalized SPDIs in [14]. Those are SPDIs not satisfying the goodness assumption (the dynamics of a region of the SPDI do not allow a trajectory to traverse an edge in opposite directions).…”