Symbolic Analysis of Hybrid Systems Involving Numerous Discrete Changes Using Loop Detection
Hybrid systems are dynamical systems that include both continuous and discrete changes. Some hybrid systems involve a large or infinite number of discrete changes within an infinitesimal-width region of phase space. Systems with sliding mode are typical examples of such hybrid systems. It is difficult to analyze such hybrid systems through ordinary numerical simulation, since the time required for simulation increases in proportion to the number of discrete changes. In this paper, we propose a method to symbolically analyze such models involving numerous discrete changes by detecting loops and checking loop invariants of the model’s behavior. The method handles parameterized hybrid systems and checks inclusion of parameterized states focusing on the values of a switching function that dominate the dynamics of sliding mode. We implemented the main part of the method in our symbolic hybrid system simulator HyLaGI, and conducted analysis of example models.
KeywordsHybrid systems Sliding mode Loop invariants Verification Symbolic analysis
- 1.Aljarbouh, A., Caillaud, B.: Chattering-free simulation of hybrid dynamical systems with the Functional Mock-Up Interface 2.0. In: Proceedings of 1st Japanese Modelica Conference, Linköping Electronic Conference Proceedings, vol. 124, no. 013, pp. 95–105 (2016)Google Scholar
- 2.Betsuno, K., Matsumoto, S., Wakatsuki, Y., Ueda, K.: Analysis of hybrid systems involving numerous discrete changes using loop detection. In: Proceedings of 30th Annual Conference of the Japanese Society for Artificial Intelligence, 1F3-4 (2016). (in Japanese)Google Scholar
- 4.Henzinger, T.: The theory of hybrid automata. In: Proceedings of LICS 1996, pp. 278–292. IEEE Computer Society Press (1996)Google Scholar
- 10.Ueda, K., Matsumoto, S., Takeguchi, A., Hosobe, H., Ishii, D.: HydLa: a high-level language for hybrid systems. In: Proceedings of 2nd Workshop on Logics for System Analysis (LfSA 2012, affiliated with CAV 2012), pp. 3–17 (2012)Google Scholar
- 12.Wakatsuki, Y., Matsumoto, S., Ueda, K.: Introduction of LTL model checking to a hybrid constraint system HyLaGI. In: Proceedings of 30th Annual Conference of the Japanese Society for Artificial Intelligence, 1F3-1 (2016). (in Japanese)Google Scholar