Article

Safety verification for probabilistic hybrid systems

Authors:

Stefan Ratschan,

Holger Hermanns,

Ernst Moritz HahnAuthors Info & Claims

CAV'10: Proceedings of the 22nd international conference on Computer Aided Verification

Pages 196 - 211

https://doi.org/10.1007/978-3-642-14295-6_21

Published: 15 July 2010 Publication History

Abstract

The interplay of random phenomena and continuous real-time control deserves increased attention for instance in wireless sensing and control applications Safety verification for such systems thus needs to consider probabilistic variations of systems with hybrid dynamics In safety verification of classical hybrid systems we are interested in whether a certain set of unsafe system states can be reached from a set of initial states In the probabilistic setting, we may ask instead whether the probability of reaching unsafe states is below some given threshold In this paper, we consider probabilistic hybrid systems and develop a general abstraction technique for verifying probabilistic safety problems This gives rise to the first mechanisable technique that can, in practice, formally verify safety properties of non-trivial continuous-time stochastic hybrid systems—without resorting to point-wise discretisation Moreover, being based on arbitrary abstractions computed by tools for the analysis of non-probabilistic hybrid systems, improvements in effectivity of such tools directly carry over to improvements in effectivity of the technique we describe We demonstrate the applicability of our approach on a number of case studies, tackled using a prototypical implementation.

References

[1]

Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems Theoretical Computer Science 138, 3-34 (1995)

Digital Library

[2]

Preußig, J., Kowalewski, S., Wong-Toi, H., Henzinger, T.: An algorithm for the approximative analysis of rectangular automata In: Ravn, A.P., Rischel, H (eds.) FTRTFT 1998 LNCS, vol 1486, p 228 Springer, Heidelberg (1998)

Digital Library

[3]

Clarke, E., Fehnker, A., Han, Z., Krogh, B., Stursberg, O., Theobald, M.: Verification of hybrid systems based on counterexample-guided abstraction refinement In: Garavel, H., Hatcliff, J (eds.) TACAS 2003 LNCS, vol 2619, pp 192-207 Springer, Heidelberg (2003)

Digital Library

[4]

Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement ACM Transactions on Embedded Computing Systems 6 (2007)

Digital Library

[5]

Altman, E., Gaitsgory, V.: Asymptotic optimization of a nonlinear hybrid system governed by a markov decision process SIAM Journal of Control and Optimization 35, 2070-2085 (1997)

Digital Library

[6]

Sproston, J.: Decidable model checking of probabilistic hybrid automata In: Joseph, M (ed.) FTRTFT 2000 LNCS, vol 1926, pp 31-45 Springer, Heidelberg (2000)

Digital Library

[7]

Bujorianu, M.L.: Extended stochastic hybrid systems and their reachability problem In: Alur, R., Pappas, G.J (eds.) HSCC 2004 LNCS, vol 2993, pp 234-249 Springer, Heidelberg (2004)

[8]

Bujorianu, M.L., Lygeros, J., Bujorianu, M.C.: Bisimulation for general stochastic hybrid systems In: Morari, M., Thiele, L (eds.) HSCC 2005 LNCS, vol 3414, pp 198-214 Springer, Heidelberg (2005)

Digital Library

[9]

Abate, A., Prandini, M., Lygeros, J., Sastry, S.: Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems Automatica 44, 2724-2734 (2008)

Digital Library

[10]

Blom, H., Lygeros, J.: Stochastic Hybrid Systems: Theory and Safety Critical Applications Lecture Notes in Control and Information Sciences, vol 337 Springer, Heidelberg (2006)

[11]

Fränzle, M., Hermanns, H., Teige, T.: Stochastic satisfiability modulo theory: A novel technique for the analysis of probabilistic hybrid systems In: Egerstedt, M., Mishra, B (eds.) HSCC 2008 LNCS, vol 4981, pp 172-186 Springer, Heidelberg (2008)

Digital Library

[12]

Teige, T., Fränzle, M.: Constraint-based analysis of probabilistic hybrid systems In: ADHS (2009)

[13]

Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes Nordic Journal of Computing 2, 250-273 (1995)

Digital Library

[14]

Alur, R., Dang, T., Ivancic, F.: Predicate abstraction for reachability analysis of hybrid systems ACM Transactions on Embedded Computing Systems 5, 152-199 (2006)

Digital Library

[15]

D'Argenio, P.R., Jeannet, B., Jensen, H.E., Larsen, K.G.: Reachability analysis of probabilistic systems by successive refinements In: de Luca, L., Gilmore, S (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001 LNCS, vol 2165, pp 39-56 Springer, Heidelberg (2001)

Digital Library

[16]

Hermanns, H., Wachter, B., Zhang, L.: Probabilistic CEGAR In: Gupta, A., Malik, S (eds.) CAV 2008 LNCS, vol 5123, pp 162-175 Springer, Heidelberg (2008)

Digital Library

[17]

Frehse, G.: Phaver: Algorithmic verification of hybrid systems past hytech In: Morari, M., Thiele, L (eds.) HSCC 2005 LNCS, vol 3414, pp 258-273 Springer, Heidelberg (2005)

Digital Library

[18]

Kwiatkowska, M.Z., Norman, G., Segala, R., Sproston, J.: Automatic verification of realtime systems with discrete probability distributions Theoretical Computer Science 282, 101-150 (2002)

Digital Library

[19]

Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.:What's decidable about hybrid automata Journal of Computer and System Sciences 57, 94-124 (1998)

Digital Library

[20]

Lafferriere, G., Pappas, G.J., Yovine, S.: A new class of decidable hybrid systems In: Vaandrager, F.W., van Schuppen, J.H (eds.) HSCC 1999 LNCS, vol 1569, pp 137-151 Springer, Heidelberg (1999)

Digital Library

[21]

Kwiatkowska, M., Norman, G., Parker, D.: Stochastic games for verification of probabilistic timed automata In: Ouaknine, J., Vaandrager, F.W (eds.) FORMATS 2009 LNCS, vol 5813, pp 212-227 Springer, Heidelberg (2009)

Digital Library

[22]

Davis, M.: Markov Models and Optimization Chapman & Hall, Boca Raton (1993)

[23]

Arnold, L.: Stochastic Differential Equations: Theory and Applications.Wiley - Interscience, Chichester (1974)

[24]

Hu, J., Lygeros, J., Sastry, S.: Towars a theory of stochastic hybrid systems In: Lynch, N.A., Krogh, B.H (eds.) HSCC 2000 LNCS, vol 1790, pp 160-173 Springer, Heidelberg (2000)

Digital Library

[25]

Bujorianu, M.L., Lygeros, J.: Toward a general theory of stochastic hybrid systems In: Stochastic Hybrid Systems Theory and Safety Critical Applications, pp 3-30 (2006)

[26]

Julius, A.A.: Approximate abstraction of stochastic hybrid automata In: Hespanha, J.P., Tiwari, A (eds.) HSCC 2006 LNCS, vol 3927, pp 318-332 Springer, Heidelberg (2006)

Digital Library

[27]

Bujorianu, M.L., Lygeros, J., Langerak, R.: Reachability analysis of stochastic hybrid systems by optimal control In: Egerstedt, M., Mishra, B (eds.) HSCC 2008 LNCS, vol 4981, pp 610-613 Springer, Heidelberg (2008)

Digital Library

[28]

Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes In: LICS, pp 266-277 (1991)

Cited By

Lal RPrabhakar P(2019)Counterexample Guided Abstraction Refinement for Polyhedral Probabilistic Hybrid SystemsACM Transactions on Embedded Computing Systems10.1145/335821718:5s(1-23)Online publication date: 8-Oct-2019
https://dl.acm.org/doi/10.1145/3358217
Huang CChen XLin WYang ZLi X(2017)Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier CertificatesACM Transactions on Embedded Computing Systems10.1145/312650816:5s(1-19)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126508
Peng YWang SZhan NZhang L(2015)Extending Hybrid CSP with Probability and StochasticityProceedings of the First International Symposium on Dependable Software Engineering: Theories, Tools, and Applications - Volume 940910.1007/978-3-319-25942-0_6(87-102)Online publication date: 4-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-25942-0_6
Show More Cited By

Recommendations

Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier Certificates
Special Issue ESWEEK 2017, CASES 2017, CODES + ISSS 2017 and EMSOFT 2017

The problem of probabilistic safety verification of stochastic hybrid systems is to check whether the probability that a given system will reach an unsafe region from certain initial states can be bounded by some given probability threshold. The paper ...
Deductive probabilistic verification methods of safety, liveness and nonzenoness for distributed real-time systems
ICESS'05: Proceedings of the Second international conference on Embedded Software and Systems

Recently, model-checking and probabilistic timed simulation verification methods of probabilistic timed automata have been developed. In this paper, we propose probabilistic timed transition systems by generalizing probabilistic timed automata, and ...
Scalable Safety Verification of Stochastic Hybrid Systems

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

CAV'10: Proceedings of the 22nd international conference on Computer Aided Verification

July 2010

673 pages

ISBN:364214294X

Editors:
Tayssir Touili
LIAFA, CNRS and University Paris Diderot, Paris Cedex 13, France
,
Byron Cook
LIAFA, Microsoft Research, Roger Needham Building, J J Thomson Avenue, Cambridge, UK
,
Paul Jackson
School of Informatics, University of Edinburgh, Roger Needham Building, J J Thomson Avenue, Edinburgh, UK

Sponsors

EPSRC: Engineering and Physical Sciences Research Council
NEC
Jasper Design Automation: Jasper Design Automation
IBMR: IBM Research
Microsoft Research: Microsoft Research

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 July 2010

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Lal RPrabhakar P(2019)Counterexample Guided Abstraction Refinement for Polyhedral Probabilistic Hybrid SystemsACM Transactions on Embedded Computing Systems10.1145/335821718:5s(1-23)Online publication date: 8-Oct-2019
https://dl.acm.org/doi/10.1145/3358217
Huang CChen XLin WYang ZLi X(2017)Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier CertificatesACM Transactions on Embedded Computing Systems10.1145/312650816:5s(1-19)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126508
Peng YWang SZhan NZhang L(2015)Extending Hybrid CSP with Probability and StochasticityProceedings of the First International Symposium on Dependable Software Engineering: Theories, Tools, and Applications - Volume 940910.1007/978-3-319-25942-0_6(87-102)Online publication date: 4-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-25942-0_6
Ghasemieh HRemke AHaverkort B(2014)Hybrid Petri nets with multiple stochastic transition firingsProceedings of the 8th International Conference on Performance Evaluation Methodologies and Tools10.4108/icst.valuetools.2014.258204(217-224)Online publication date: 9-Dec-2014
https://dl.acm.org/doi/10.4108/icst.valuetools.2014.258204
Hahn EHermanns HBelta CIvančić F(2013)Rewarding probabilistic hybrid automataProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461375(313-322)Online publication date: 8-Apr-2013
https://dl.acm.org/doi/10.1145/2461328.2461375
Kamgarpour MSummers SLygeros JBelta CIvančić F(2013)Control design for specifications on stochastic hybrid systemsProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461374(303-312)Online publication date: 8-Apr-2013
https://dl.acm.org/doi/10.1145/2461328.2461374
Abate AKatoen JMereacre ACaccamo MFrazzoli EGrosu R(2011)Quantitative automata model checking of autonomous stochastic hybrid systemsProceedings of the 14th international conference on Hybrid systems: computation and control10.1145/1967701.1967715(83-92)Online publication date: 12-Apr-2011
https://dl.acm.org/doi/10.1145/1967701.1967715
Fränzle MHahn EHermanns HWolovick NZhang LCaccamo MFrazzoli EGrosu R(2011)Measurability and safety verification for stochastic hybrid systemsProceedings of the 14th international conference on Hybrid systems: computation and control10.1145/1967701.1967710(43-52)Online publication date: 12-Apr-2011
https://dl.acm.org/doi/10.1145/1967701.1967710
Fränzle MTeige TEggers A(2010)Satisfaction meets expectationsProceedings of the 8th international conference on Integrated formal methods10.5555/1929463.1929476(168-182)Online publication date: 11-Oct-2010
https://dl.acm.org/doi/10.5555/1929463.1929476
Assouramou JDesharnais J(2010)Continuous time and/or continuous distributionsProceedings of the 7th European performance engineering conference on Computer performance engineering10.5555/1926981.1926991(99-114)Online publication date: 23-Sep-2010
https://dl.acm.org/doi/10.5555/1926981.1926991

View Options

View options

Media

Figures

Other

Tables

View Table of Contents