Abstract
A hybrid system models both discrete event and continuous dynamics. We present a modeling formalism and a verification methodology for hybrid systems. The verification methodology is based on abstracting the continuous dynamics in the hybrid system by simpler continuous dynamics. We present two methods for doing this: in the first method, a differential inclusion is replaced with a simpler differential inclusion; in the second method, we look at the timing information that is relevant to the verification problem, and construct an abstraction of the hybrid system with a timed automaton. We illustrate our methodology by applying it to the train-gate-controller example.
Research supported by the California PATH program and by the National Science Foundation under grant ECS9417370.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R.Alur, C.Courcoubetis, T.A. Henzinger and P.-H. Ho, Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems, Hybrid Systems, LNCS 736, Springer-Verlag.
R. Alur and D. Dill, Automata for modeling real-time systems, Proc. 17th ICALP, LNCS 443, Springer-Verlag, 1990.
R.Alur, A.Itai, R.Kurshan and M.Yannakakis, Timing Verification by Successive Approximation, Proc. 4th Workshop Computer-Aided Verification, Lecture Notes in Computer Science 663, Springer-Verlag, 1992.
P.Kopke, T. Henzinger, A. Puri and P. Varaiya, What's Decidable About Hybrid Automata, STOCS 1995.
R.L. Grossman et al., eds., Hybrid Systems, LNCS 736, Springer-Verlag, 1993.
X.Nicollin, A. Olivero, J. Sifakis, and S.Yovine, An Approach to the Description and Analysis of Hybrid Systems, Hybrid Systems, LNCS 736, Springer-Verlag, 1993.
A. Puri and P. Varaiya, Decidability of Hybrid Systems with Rectangular Differential Inclusions, Computer-Aided Verification 1994, LNCS 818, Springer-Verlag, 1994.
A. Puri and P. Varaiya, Driving Safely in Smart Cars, American Control Conference 1995.
A. Puri, V. Borkar, and P. Varaiya, e-Approximation of Differential Inclusions, Draft.
P.Varaiya. Smart Cars on Smart Roads: Problems of Control. IEEE Transactions on Automatic Control, 38(2):195–207, February 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Puri, A., Varaiya, P. (1995). Verification of hybrid systems using abstractions. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems II. HS 1994. Lecture Notes in Computer Science, vol 999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60472-3_18
Download citation
DOI: https://doi.org/10.1007/3-540-60472-3_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60472-3
Online ISBN: 978-3-540-47519-4
eBook Packages: Springer Book Archive