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
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 CWI
Series Modelling, Analysis and Simulation [MAS]
Project Computational Topology for Systems and Control
Note This research was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) Vidi grant 639.032.408.
Citation
Collins, P.J. (2008). Computing controllable sets of hybrid systems. Modelling, Analysis and Simulation [MAS]. CWI.