Abstract
Average dwell time (ADT) properties characterize the rate at which a hybrid system performs mode switches. In this article, we present a set of techniques for verifying ADT properties. The stability of a hybrid system A can be verified by combining these techniques with standard methods for checking stability of the individual modes of A.
We introduce a new type of simulation relation for hybrid automata—switching simulation—for establishing that a given automaton A switches more rapidly than another automaton B. We show that the question of whether a given hybrid automaton has ADT τa can be answered either by checking an invariant or by solving an optimization problem. For classes of hybrid automata for which invariants can be checked automatically, the invariant-based method yields an automatic method for verifying ADT; for automata that are outside this class, the invariant has to be checked using inductive techniques. The optimization-based method is automatic and is applicable to a restricted class of initialized hybrid automata. A solution of the optimization problem either gives a counterexample execution that violates the ADT property, or it confirms that the automaton indeed satisfies the property. The optimization and the invariant-based methods can be used in combination to find the unknown ADT of a given hybrid automaton.
- Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T. A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., and Yovine, S. 1995. The algorithmic analysis of hybrid systems. Theor. Comput. Sci. 138, 1, 3--34. Google Scholar
Digital Library
- Alur R. and Henzinger, T. A., Eds. 1996. Verification of an audio protocol with bus collision using UPPAAL. In Proceedings of the 8th International Conference on Computer-Aided Verification (CAV'96). Springer-Verlag, Berlin, 411--414. Google Scholar
Digital Library
- Alur, R., Henzinger, C. C. T. A., and Ho., P. H. 1993. Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds. Hybrid Systems. Lecture Notes in Computer Science, vol. 736. Springer-Verlag, 209--229. Google Scholar
Digital Library
- Alur, R. and Pappas, G. J., Eds. 2004. Hybrid systems: computation and control. In Proceedings of the 7th International Workshop (HSCC'04). Springer, Berlin.Google Scholar
- Archer, M. 2001. TAME: PVS Strategies for special purpose theorem proving. Annals Math. AI 29, 1/4. Google Scholar
Digital Library
- Bayen, A. M., Cruck, E., and Tomlin, C. 2002. Guaranteed overapproximations of unsafe sets for continuous and hybrid systems: solving the hamilton-jacobi equation using viability techniques. In Proceedings of the 5th International Workshop (HSCC'02), Springer, Berlin. Google Scholar
Digital Library
- Bemporad, A., Bicchi, A., and Buttazzo, G. C., Eds. 2007. Proceedings of the 10th International Workshop, (HSCC'07). Springer, Berlin.Google Scholar
- Bemporad, A. and Morari, M. 1999. Verification of hybrid systems via mathematical programming. In Proceedings of the 2nd International Workshop on Hybrid Systems: Computation and Control (HSCC'99). Springer, Berlin, 31--45. Google Scholar
Digital Library
- Branicky, M. 1995. Studies in hybrid systems: modeling, analysis, and control. Ph.D. Thesis, MIT, Cambridge, MA. Google Scholar
Digital Library
- Branicky, M. 1998. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Auto. Control 43, 475--482.Google Scholar
Cross Ref
- Branicky, M., Borkar, V., and Mitter, S. 1998. A unified framework for hybrid control: Model and optimal control theory. IEEE Trans. Auto. Control 43, 1, 31--45.Google Scholar
Cross Ref
- Chatterjee, D. and Liberzon, D. 2006. Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions. SIAM J. Control Optimiz. 45, 1, 174--206. Google Scholar
Digital Library
- Cormen, T. H., Leiserson, C. E., and Rivest, R. L. 1990. Introduction to Algorithms. MIT Press/McGraw-Hill, Cambridge, MA. Google Scholar
Digital Library
- Cruz, R. L. 1991. A calculus for network delay, part i: Network elements in isolation. IEEE Trans. Inform. Theory 37, 1, 114--131.Google Scholar
Digital Library
- Floyd, R. 1967. Assigning meanings to programs. In Proceedings of the Symposium on Applied Mathematics. Mathematical Aspects of Computer Science. American Mathematical Society, 19--32.Google Scholar
Cross Ref
- Frehse, G. 2005. Phaver: algorithmic verification of hybrid systems past hytech. In Proceedings of the 8th International Workshop on Hybrid Systems: Computation and Control (HSCC'05). Springer, Berlin.Google Scholar
Digital Library
- GNU. GLPK—GNU linear programming kit. http://www.gnu.org/directory/libs/glpk.html.Google Scholar
- Heitmeyer, C. and Lynch, N. 1994. The generalized railroad crossing: A case study in formal verification of real-time system. In Proceedings of the 15th IEEE Real-Time Systems Symposium, (San Juan, Puerto Rico). IEEE, Los Alamitos, CA.Google Scholar
- Henzinger, T. A., Ho, P.-H., and Wong-Toi, H. 1997. Hytech: A model checker for hybrid systems. In Proceedings of the 9th International Conference on Computer Aided Verification (CAV'97). Springer, Berlin, 460--483. Google Scholar
Digital Library
- Henzinger, T. A. and Kopke, P. W. 1996. State equivalences for rectangular hybrid automata. In Proceedings of the International Conference on Concurrency Theory (CONCUR'96). Springer, Berlin, 530--545. Google Scholar
Digital Library
- Henzinger, T. A., Kopke, P. W., Puri, A., and Varaiya, P. 1995. What' decidable about hybrid automata? In Proceedings of the 27th Annual ACM Symposium on Theory of Computing (SOTC'95). ACM, New York, 373--382. Google Scholar
Digital Library
- Henzinger, T. A. and Majumdar, R. 2000. Symbolic model checking for rectangular hybrid systems. In Proceedings of the 6th International Workshop on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'00). Springer, Berlin, 142--156. Google Scholar
Digital Library
- Hespanha, J., Liberzon, D., and Morse, A. 2003. Hysteresis-based switching algorithms for supervisory control of uncertain systems. Automatica 39, 263--272.Google Scholar
Digital Library
- Hespanha, J. and Morse, A. 1999. Stability of switched systems with average dwell-time. In Proceedings of 38th IEEE Conference on Decision and Control. IEEE, Los Alamitos, CA, 2655--2660.Google Scholar
- Hespanha, J. P. and Tiwari, A., Eds. 2006. Proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control (HSCC'06). Springer, Berlin.Google Scholar
- Khalil, H. K. 2002. Nonlinear Systems 3rd Ed. Prentice Hall, Upper Saddle River, NJ.Google Scholar
- Kurzhanski, A. B. and Varaiya, P. 2000. Ellipsoidal techniques for reachability analysis. In Proceedings of the 3rd International Workshop on Hybrid Systems: Computation and Control (HSCC'00). Springer, Berlin, 202--214. Google Scholar
Digital Library
- Lafferriere, G., Pappas, G. J., and Yovine, S. 1999. A new class of decidable hybrid systems. In Proceedings of the 2nd International Workshop on Hybrid Systems: Computation and Control (HSCC'99). Springer, Berlin, 137--151. Google Scholar
Digital Library
- Liberzon, D. 2003. Switching in Systems and Control. Systems and Control: Foundations and Applications. Birkhauser, Boston, MA.Google Scholar
- Livadas, C., Lygeros, J., and Lynch, N. A. 1999. High-level modeling and analysis of TCAS. In Proceedings of the 20th IEEE Real-Time Systems Symposium (RTSS'99). IEEE, Los Alamitos, CA, 115--125. Google Scholar
Digital Library
- Lynch, N. 1996. A three-level analysis of a simple acceleration maneuver, with uncertainties. In Proceedings of the 3rd AMAST Workshop on Real-Time Systems. World Scientific Publishing Company, Mountain View, CA, 1--22.Google Scholar
- Lynch, N., Segala, R., and Vaandrager, F. 2003. Hybrid I/O automata. Inform. Compu. 185, 1, 105--157. Google Scholar
Digital Library
- Lynch, N. and Vaandrager, F. 1996. Forward and backward simulations—part II: Timingbased systems. Inform. Comput. 128, 1, 1--25. Google Scholar
Digital Library
- Maler, O. and Pnueli, A., Eds. 2003. Proceedings of the 6th International Workshop on Hybrid Systems: Computation and Control (HSCC'03). Springer, Berlin.Google Scholar
- Mitchell, I. and Tomlin, C. 2000. Level set methods for computation in hybrid systems. In Proceedings of the 3rd International Workshop on Hybrid Systems: Computation and Control (HSCC'00). Springer, Berlin, 310--323. Google Scholar
Digital Library
- Mitra, S. 2007. A verification framework for hybrid systems. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. Google Scholar
Digital Library
- Mitra, S. and Archer, M. 2005. PVS strategies for proving abstraction properties of automata. Electronic Notes Theore. Comput. Sci. 125, 2, 45--65.Google Scholar
Digital Library
- Mitra, S. and Lynch, N. A. 2007. Trace-based semantics for probabilistic timed i/o automata. In Proceedings of the 10th International Workshop (HSCC'07), (Pisa, Italy), April 3--5. Springer, Berlin, 718--722.Google Scholar
- Mitra, S., Wang, Y., Lynch, N., and Feron, E. 2003. Safety verification of model helicopter controller using hybrid Input/Output automata. In Proceedings of the 6th International Workshop on Hybrid Systems: Computation and Control (HSCC'03). Springer, Berlin, 343--358.Google Scholar
- Morari, M. and Thiele, L., Eds. 2005. Proceedings of the 8th International Workshop on Hybrid Systems: Computation and Control (HSCC'05). Springer, Berlin.Google Scholar
- Morse, A. S. 1996. Supervisory control of families of linear set-point controllers, part 1: Exact matching. IEEE Trans. Auto. Control 41, 1413--1431.Google Scholar
Cross Ref
- Owre, S., Rajan, S., Rushby, J., Shankar, N., and Srivas, M. 1996. PVS: Combining specification, proof checking, and model checking. In Proceedings of Computer-Aided Verification (CAV'96). Google Scholar
Digital Library
- Prajna, S. and Jadbabaie, A. 2004. Safety verification of hybrid systems using barrier certificates. In Proceedings of the 7th International Workshop on Hybrid Systems: Computation and Control (HSCC'04). Springer, Berlin.Google Scholar
- Tomlin, C. and Greenstreet, M. R., Eds. 2002. Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control (HSCC'02). Springer, Berlin. Google Scholar
Digital Library
- Umeno, S. and Lynch, N. A. 2007. Safety verification of an aircraft landing protocol: A refinement approach. In Proceedings of the 10th International Workshop, (HSCC'07). Springer, Berlin, 557--572.Google Scholar
- van der Schaft, A. and Schumacher, H. 2000. An Introduction to Hybrid Dynamical Systems. Springer, Berlin.Google Scholar
- Vu, L., Chatterjee, D., and Liberzon, D. 2007. Input-to-state stability of switched systems and switching adaptive control. Automatica 43, 4, 639--646. Google Scholar
Digital Library
- Weinberg, H. B. and Lynch, N. 1996. Correctness of vehicle control systems—a case study. In Proceeding of the 17th IEEE Real-Time Systems Symposium. IEEE, Los Alamitos, CA, 62--72. Google Scholar
Digital Library
- Weinberg, H. B., Lynch, N., and Delisle, N. 1995. Verification of automated vehicle protection systems. In Proceedings of the 3rd International Workshop on Hybrid Systems III: Verification and Control Workshop on Verification and Control of Hybrid Systems. Springer, Berlin, 101--113. Google Scholar
Digital Library
- Williams, H. 1990. Model Building in Mathematical Programming 3rd Ed. John Wiley, New York.Google Scholar
- Zhai, G., Hu, B., Yasuda, K., and Michel, A. 2000. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. In Proceedings of the American Control Conference (AACC).Google Scholar
Index Terms
Verifying average dwell time of hybrid systems
Recommendations
Verifying cyber-physical systems by combining software model checking with hybrid systems reachability
EMSOFT '16: Proceedings of the 13th International Conference on Embedded SoftwareCyber-physical systems (CPS) span the communication, computation and control domains. Creating a single, complete, and detailed model of a CPS is not only difficult, but, in terms of verification, probably not useful; current verification algorithms are ...
Time-aware relational abstractions for hybrid systems
EMSOFT '13: Proceedings of the Eleventh ACM International Conference on Embedded SoftwareHybrid Systems model both discrete switches and continuous dynamics and are suitable to represent embedded systems where discrete controllers interact with a physical plant.
Relational abstraction is a new approach for verifying hybrid systems. In ...
Generalized Property-Directed Reachability for Hybrid Systems
Verification, Model Checking, and Abstract InterpretationAbstractGeneralized property-directed reachability (GPDR) belongs to the family of the model-checking techniques called IC3/PDR. It has been successfully applied to software verification; for example, it is the core of Spacer, a state-of-the-art Horn-...






Comments