Relaxing goodness is still good. (English) Zbl 1161.93316

Pace, Gordon J.; Schneider, Gerardo

Fitzgerald, John S. (ed.) et al., Theoretical aspects of computing – ICTAC 2008. 5th international colloquium, Istanbul, Turkey, September 1–3, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85761-7/pbk). Lecture Notes in Computer Science 5160, 274-289 (2008).

Summary: 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 assumption – which 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 assumption, and give an algorithmic solution to decide reachability of such systems.
For the entire collection see [Zbl 1154.68011].

MSC:

93C30	Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
34A60	Ordinary differential inclusions
93B03	Attainable sets, reachability

Keywords:

polygonal hybrid systems; differential inclusions; reachability problem