Safety verification of hybrid systems by constraint propagation based abstraction refinement. (English) Zbl 1078.93508

Ratschan, Stefan; She, Zhikun

Morari, Manfred (ed.) et al., Hybrid systems: Computation and control. 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9–11, 2005. Proceedings. Berlin: Springer (ISBN 3-540-25108-1/pbk). Lecture Notes in Computer Science 3414, 573-589 (2005).

Summary: This paper deals with the problem of safety verification of non-linear hybrid systems. We start from a classical method that uses interval arithmetic to check whether trajectories can move over the boundaries in a rectangular grid. We put this method into an abstraction refinement framework and improve it by developing an additional refinement step that employs constraint propagation to add information to the abstraction without introducing new grid elements. Moreover, the resulting method allows switching conditions, initial states and unsafe states to be described by complex constraints instead of sets that correspond to grid elements. Nevertheless, the method can be easily implemented since it is based on a well-defined set of constraints, on which one can run any constraint propagation based solver. First tests of such an implementation are promising.
For the entire collection see [Zbl 1069.68011].

MSC:

93B03	Attainable sets, reachability
93C30	Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
68Q60	Specification and verification (program logics, model checking, etc.)

Software:

PHAVer; Benchmarks; QEPCAD; RSOLVER; d/dt; HSolver