Reachability in linear dynamical systems

Emmanuel Hainry 1
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : Dynamical systems allow to modelize various phenomena or processes by only describing their local behaviour. It is however useful to understand the behaviour in a more global way. Checking the reachability of a point for example is a fundamental problem. In this document we will show that this problem that is undecidable in the general case is in fact decidable for a natural class of continuous-time dynamical systems: linear systems. For this, we will use results from the algebraic numbers theory such as Gelfond-Schneider's theorem.
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Communication dans un congrès
Beckmann, Arnold and Dimitracopoulos, Costas and Lwe, Benedikt. Computability in Europe, Jun 2008, Athènes, Greece. Springer, 5028, pp.241-250, 2008, Lecture Notes in Computer Sciences. 〈10.1007/978-3-540-69407-6_28〉
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Emmanuel Hainry. Reachability in linear dynamical systems. Beckmann, Arnold and Dimitracopoulos, Costas and Lwe, Benedikt. Computability in Europe, Jun 2008, Athènes, Greece. Springer, 5028, pp.241-250, 2008, Lecture Notes in Computer Sciences. 〈10.1007/978-3-540-69407-6_28〉. 〈inria-00202674v2〉

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