Control of Hidden Mode Hybrid Systems: Algorithm termination

We consider the problem of safety control in Hidden Mode Hybrid Systems (HMHS) that arises in the development of a semi-autonomous cooperative active safety system for collision avoidance at an intersection. We utilize the approach of constructing a new hybrid automaton whose discrete state is an estimate of the HMHS mode. A dynamic feedback map can then be designed that guarantees safety on the basis of the current mode estimate and the concept of the capture set. In this work, we relax the conditions for the termination of the algorithm that computes the capture set by constructing an abstraction of the new hybrid automaton. We present a relation to compute the capture set for the abstraction and show that this capture set is equal to the one for the new hybrid automaton.