In this paper we consider the controllability problem for hybrid systems, namely that of determining the set of states which can be driven into a given target set. We show that given a suitable definition of controllability, we can effectively compute arbitrarily accurate under-approximations to the controllable set using Turing machines. However, due to grazing or sliding along guard sets, we see that it may be able to demonstrate that an initial state can be controlled to the target set, without knowing any trajectory which solves the problem.

Additional Metadata
Keywords Hybrid system, controllable set, computable analysis, safety.
MSC Attainable sets (msc 93B03), Explicit machine computation and programs (not the theory of computation or programming) (msc 93-04), Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (msc 68Q17), Computational methods (msc 93B40)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher European Union Control Association
Editor J. Bokor
Project Computational Topology for Systems and Control
Conference European Control Conference
Citation
Collins, P.J. (2009). Controllability and Falsification of Hybrid Systems. In J Bokor (Ed.), Proceedings of the European Control Conference 2009. European Union Control Association.