Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods
Aiming at automatic verification and analysis techniques for hybrid systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art enclosure method for ODEs, and with bracketing systems which exploit monotonicity properties to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply our method to the analysis of a non-linear hybrid system by solving predicative encodings of an inductive stability argument and evaluate the impact of different methods and their combination.
KeywordsHybrid System Proof Obligation Arithmetic Constraint Current Partial Assignment Delta Time
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- 1.Berz, M.: COSY INFINITY version 8 reference manual. Tech. Rep. MSUCL–1088, National Superconducting Cyclotron Lab., Michigan State University, USA (1997)Google Scholar
- 8.Ishii, D., Ueda, K., Hosobe, H.: An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems. International Journal on Software Tools for Technology Transfer (STTT), 1–13 (March 2011)Google Scholar
- 9.Ishii, D., Ueda, K., Hosobe, H., Goldsztejn, A.: Interval-based solving of hybrid constraint systems. In: Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems, pp. 144–149 (2009)Google Scholar
- 10.Kieffer, M., Walter, E., Simeonov, I.: Guaranteed nonlinear parameter estimation for continuous-time dynamical models. In: Proceedings 14th IFAC Symposium on System Identification, Newcastle, Aus, pp. 843–848 (2006)Google Scholar
- 12.Nedialkov, N.S.: VNODE-LP — a validated solver for initial value problems in ordinary differential equations. Tech. Rep. CAS-06-06-NN, Department of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4K1 (2006), VNODE-LP http://www.cas.mcmaster.ca/~nedialk/vnodelp
- 14.Nedialkov, N.S.: Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation. Ph.D. thesis, Department of Computer Science, University of Toronto, Toronto, Canada, M5S 3G4 (February 1999)Google Scholar
- 18.Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. ACM Transactions in Embedded Computing Systems 6(1) (2007)Google Scholar