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The algorithmic analysis of hybrid systems
Open accessAbstract
We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as finite automata equipped with variables that evolve continuously with time according to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard program-analysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.
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Cites
Cousot, P., & Cousot, R. (1977) · Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '77 · doi:10.1145/512950.512973 · Cited by 6,279
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Gerkey, B. P., & Matarić, M. J. (2004) · The International Journal of Robotics Research · doi:10.1177/0278364904045564 · Cited by 1,753
A survey of computational complexity results in systems and control
Blondel, V. D., & Tsitsiklis, J. N. (2000) · Automatica · doi:10.1016/s0005-1098(00)00050-9 · Cited by 732
Integrated Task and Motion Planning
Garrett, C. R., Chitnis, R., Holladay, R., Kim, B., Silver, T., Kaelbling, L. P., & Lozano-Pérez, T. (2021) · Annual Review of Control, Robotics, and Autonomous Systems · doi:10.1146/annurev-control-091420-084139 · Cited by 409
Gomes, C., Thule, C., Broman, D., Larsen, P. G., & Vangheluwe, H. (2019) · ACM Computing Surveys · doi:10.1145/3179993 · Cited by 369
Computational techniques for the verification of hybrid systems
Tomlin, C. J., Mitchell, I., Bayen, A. M., & Oishi, M. (2003) · Proceedings of the IEEE · doi:10.1109/jproc.2003.814621 · Cited by 353
Metadata
- Authors
- Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T. A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., & Yovine, S.
- Venue
- Theoretical Computer Science
- Publisher
- Elsevier BV
- Published
- 1995-02
- Volume
- 138
- Issue
- 1
- Pages
- 3-34
- ISSN
- 0304-3975 (ISSN-L)
- OpenAlex
- W2004463571
- Cited by
- 1,876
- References
- 1
- FWCI
- 71.40
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T. A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., & Yovine, S. (1995). The algorithmic analysis of hybrid systems. Theoretical Computer Science. https://doi.org/10.1016/0304-3975(94)00202-t
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