Abstract
We look at the problem of proving inevitability of continuous dynamical systems. An inevitability property says that a region of the state space will eventually be reached: this is a type of liveness property from the computer science viewpoint, and is related to attractivity of sets in dynamical systems. We consider a method of Maler and Batt to make an abstraction of a continuous dynamical system to a timed automaton, and show that a potentially infinite number of splits will be made if the splitting of the state space is made arbitrarily. To solve this problem, we define a method which creates a finite-sized timed automaton abstraction for a class of linear dynamical systems, and show that this timed abstraction proves inevitability.
This paper has been made under the framework of the EPSRC-funded project “DYVERSE: A New Kind of Control for Hybrid Systems” (EP/I001689/1). The second author is also grateful for the support of the RCUK (EP/E50048/1).
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Carter, R., Navarro-López, E.M. (2012). Dynamically-Driven Timed Automaton Abstractions for Proving Liveness of Continuous Systems. In: Jurdziński, M., Ničković, D. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2012. Lecture Notes in Computer Science, vol 7595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33365-1_6
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