Constraints for Continuous Reachability in the Verification of Hybrid Systems
The method for verification of hybrid systems by constraint propagation based abstraction refinement that we introduced in an earlier paper is based on an over-approximation of continuous reachability information of ordinary differential equations using constraints that do not contain differentiation symbols. The method uses an interval constraint propagation based solver to solve these constraints. This has the advantage that—without complicated algorithmic changes—the method can be improved by just changing these constraints. In this paper, we discuss various possibilities of such changes, we prove some properties about the amount of over-approximations introduced by the new constraints, and provide some timings that document the resulting improvement.
Unable to display preview. Download preview PDF.
- 2.Belta, C., Schug, J., Dang, T., Kumar, V., Pappas, G., Rubin, H., Dunlap, P.: Stability and reachability analysis of a hybrid model of luminescence in the marine bacterium vibrio fisheri. In: CDC 2001 - Conference on Decision and Control, Florida, USA (2001)Google Scholar
- 6.Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, Thiele, Google Scholar
- 9.Hickey, T.J.: Metalevel interval arithmetic and verifiable constraint solving. Journal of Functional and Logic Programming 2001(7) (October 2001)Google Scholar
- 11.Puri, A., Varaiya, P.: Driving safely in smart cars. In: Proc. of the 1995 American Control Conference, pp. 3597–3599 (1995)Google Scholar
- 12.Ratschan, S.: RSolver. Software package (2004), http://rsolver.sourceforge.net
- 13.Ratschan, S.: Efficient solving of quantified inequality constraints over the real numbers. ACM Transactions on Computational Logic (to appear, 2005)Google Scholar
- 14.Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. ACM Journal in Embedded Computing Systems (to appear)Google Scholar
- 15.Ratschan, S., She, Z.: HSolver. Software package (2004), http://hsolver.sourceforge.net
- 16.Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. In: Morari, Thiele, Google Scholar