VIABILITY IN HYBRID SYSTEMS

Hybrid systems an interacting systems of digital automata and continuo us plants subject to disturbances. The digital automata are used to fo rce the state trajectory of the continuous plant to obey a performance specification. For the basic concepts and notation for hybrid systems , see Kohn and Nerode (1993), and other papers in the same volume, Her e we introduce tools for analyzing enforcing viability of all possible plant state trajectories of a hybrid system by suitable choices of fi nite state control automata. Thus, the performance specification consi dered here is that the state of the plant remain in a prescribed viabi lity set of states at all times (Aubin, 1991). The tools introduced ar e local viability graphs and viability graphs for hybrid systems. We c onstruct control automata which guarantee viability as the fixpoints o f certain operators on graphs. When control and state spaces are compa ct, the viability set is closed, and a non-empty closed subset of a vi ability graph is given with a sturdiness property, one can extract fin ite state automata guaranteeing viable trajectories. This paper is a s equel to Kohn and Nerode (1993), especially Appendix II.