Controllability and falsification of hybrid systems

Abstract

Abstract-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.

Computability and Dynamical Systems

“…The literature about computability and controllability focuses essentially on the computation of classes of "controllers" which allow the control of specific classes of systems: hybrid systems [37], [57], [16] and discrete-time semicontinuous systems [14].…”