Abstract
A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete updates with differential constraints for capturing continuous flows. Formal verification of hybrid automata relies on symbolic fixpoint computation procedures that manipulate sets of states. These procedures can be implemented using boolean combinations of linear constraints over system variables, equivalently, using polyhedra, for the subclass of linear hybrid automata. In a linear hybrid automaton, the flow at each control mode is given by a rate polytope that constrains the allowed values of the first derivatives. The key property of such a flow is that, given a state-set described by a polyhedron, the set of states that can be reached as time elapses, is also a polyhedron. We call such a flow a polyhedral flow. In this paper, we study if we can generalize the syntax of linear hybrid automata for describing flows without sacrificing the polyhedral property. In particular, we consider flows described by origin-dependent rate polytopes, in which the allowed rates depend, not only on the current control mode, but also on the specific state at which the mode was entered. We establish that flows described by origin-dependent rate polytopes, in some special cases, are polyhedral.
Supported in part by Bell Laboratories, Lucent Technologies, and by the NSF CAREER award CCR-9734115 and by the DARPA grant NAG2-1214.
Supported in part by the ARO grant DAAG55-98-1-0393 and the NSF award CCR-96-19910.
Visiting from Department of Computer Science, University of Salerno, Italy.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Alur, C. Courcoubetis, and D.L. Dill. Model-checking in dense real-time. Information and Computation, 104(1):2–34, 1993.
R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.
R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.
R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic symbolic verification of embedded systems. IEEE Transactions on Software Engineering, 22(3):181–201, 1996.
J.R. Burch, E.M. Clarke, D.L. Dill, L.J. Hwang, and K.L. McMillan. Symbolic model checking: 1020 states and beyond. Information and Computation, 98(2):142–170, 1992.
E.M. Clarke and E.A. Emerson. Design and synthesis of synchronization skeletons using branching time temporal logic. In Proc. Workshop on Logic of Programs, LNCS 131, pages 52–71. Springer-Verlag, 1981.
E.M. Clarke and R.P. Kurshan. Computer-aided verification. IEEE Spectrum, 33(6):61–67, 1996.
T.A. Henzinger, P. Ho, and H. Wong-Toi. HyTech: a model checker for hybrid systems. Software Tools for Technology Transfer, 1, 1997.
T.A. Henzinger, P. Kopke, A. Puri, and P. Varaiya. What’s decidable about hybrid automata. In Proceedings of the 27th ACM Symposium on Theory of Computing, pages 373–382, 1995.
P.H. Ho and H. Wong-Toi. Automated analysis of an audio control protocol. In Proceedings of the Seventh Conference on Computer-Aided Verification, LNCS 939, pages 381–394. Springer-Verlag, 1995.
T.A. Henzinger and H. Wong-Toi. Linear phase-portrait approximations of nonlinear hybrid systems. In Hybrid Systems III: Verification and Control, LNCS 1066, pages 377–388. Springer-Verlag, 1996.
G. Lafferriere, G. Pappas, and S. Sastry. O-minimal hybrid systems. 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alur, R., Kannan, S., La Torre, S. (1999). Polyhedral Flows in Hybrid Automata. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_5
Download citation
DOI: https://doi.org/10.1007/3-540-48983-5_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65734-7
Online ISBN: 978-3-540-48983-2
eBook Packages: Springer Book Archive