Abstract
This paper deals with conservative reachability analysis of a class of hybrid systems with continuous dynamics described by linear differential inclusions, convex invariants and guards, and linear reset maps. We present an approach for computing over-approximations of the set of reachable states. It is based on the notion of support function and thus it allows us to consider invariants, guards and constraints on continuous inputs and initial states defined by arbitrary compact convex sets. We show how the properties of support functions make it possible to derive an effective algorithm for approximate reachability analysis of hybrid systems. We use our approach on some examples including the navigation benchmark for hybrid systems verification.
This work was supported by the ANR SETIN project VAL-AMS.
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References
Chutinan, A., Krogh, B.: Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 76–90. Springer, Heidelberg (1999)
Asarin, E., Dang, T., Maler, O., Bournez, O.: Approximate reachability analysis of piecewise-linear dynamical systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 20–31. Springer, Heidelberg (2000)
Kurzhanski, A., Varaiya, P.: Ellipsoidal techniques for reachability analysis. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 202–214. Springer, Heidelberg (2000)
Botchkarev, O., Tripakis, S.: Verification of hybrid systems with linear differential inclusions using ellipsoidal approximations. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 73–88. Springer, Heidelberg (2000)
Stursberg, O., Krogh, B.: Efficient representation and computation of reachable sets for hybrid systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 482–497. Springer, Heidelberg (2003)
Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291–305. Springer, Heidelberg (2005)
Girard, A., Le Guernic, C., Maler, O.: Efficient computation of reachable sets of linear time-invariant systems with inputs. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 257–271. Springer, Heidelberg (2006)
Varaiya, P.: Reach set computation using optimal control. In: Proc. KIT Workshop on Verification of Hybrid Systems, Grenoble (1998)
Le Guernic, C., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Analysis: Hybrid Systems (2009) (to appear)
Fehnker, A., Ivancic, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004)
Bertsekas, D., Nedic, A., Ozdaglar, A.: Convex analysis and optimization. Athena Scientific (2003)
Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press, Cambridge (2004)
Rockafellar, R., Wets, R.: Variational analysis. Springer, Heidelberg (1998)
Girard, A., Le Guernic, C.: Zonotope/hyperplane intersection for hybrid systems reachability analysis. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 215–228. Springer, Heidelberg (2008)
Kiefer, J.: Sequential minimax search for a maximum. Proceedings of the American Mathematical Society 4, 502–506 (1953)
Frehse, G.: PHAVer: algorithmic verification of hybrid systems past HyTech. Int. J. on Software Tools for Technology Transfer 10(3), 263–279 (2008)
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Le Guernic, C., Girard, A. (2009). Reachability Analysis of Hybrid Systems Using Support Functions. In: Bouajjani, A., Maler, O. (eds) Computer Aided Verification. CAV 2009. Lecture Notes in Computer Science, vol 5643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02658-4_40
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DOI: https://doi.org/10.1007/978-3-642-02658-4_40
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