SPeeDI ― A Verification Tool for Polygonal Hybrid Systems

摘要

Hybrid systems combining discrete and continuous dynamics arise as mathematical models of various artificial and natural systems, and as an approximation to complex continuous systems. A very important problem in the analysis of the behavior of hybrid systems is reachability. It is well-known that for most non-trivial subclasses of hybrid systems this and all interesting verification problems are undecidable. Most of the proved decidability results rely on stringent hypothesis that lead to the existence of a finite and computable partition of the state space into classes of states which are equivalent with respect to reachability. This is the case for classes of rectangular automata and hybrid automata with linear vector fields. Most implemented computational procedures resort to (forward or backward) propagation of constraints, typically (unions of convex) polyhedra or ellipsoids. In general, these techniques provide semi-decision procedures, that is, if the given final set of states is reachable, they will terminate, otherwise they may fail to. Maybe the major drawback of set-propagation, reach-set approximation procedures is that they pay little attention to the geometric properties of the specific (class of) systems under analysis. An interesting and still decidable class of hybrid system are the (2-dimensional) polygonal differential inclusions (or SPDI for short). An SPDI (Fig. 1) is defined by giving a finite partition P of the plane into convex polygonal sets, and associating with each P ∈ P a couple of vectors a_p d_p.