Abstract not found

Abstract. In this paper, we introduce and study quotients of fully nonlinear control systems. Our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems. We show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state/input space. This allows one to understand how states and inputs of the quotient system are related to states and inputs of the original system. We also introduce a notion of projectability which turns out to be equivalent to controlled invariance. This allows one to regard previous work on symmetries, partial symmetries, and controlled invariance as leading to special types of quotients. We also show the existence of quotients that are not induced by symmetries or controlled invariance. Such decompositions have a potential use in a theory of hierarchical control based on quotients.

Using hybrid automata, one is able to model many types of systems and express their properties in various formal languages. Being extremely general and rich, however, the class of hybrid automata exhibits the inherent problems of automata theory: even the simplest of properties for general hybrid automata are undecidable. Therefore, one must restrict attention only to subclasses of this very general class. The literature to date has seemed to indicate that for a whole subclass of hybrid automata to have decidable properties it would either have to have very simple continuous dynamics (timed automata, piecewise affine inclusions, etc.) or decoupled discrete and continuous dynamics (o-minimal hybrid systems, initialized rectangular automata), where the continuous components of the system are reset in a memoryless manner after each discrete transition. The thesis of this dissertation is that this need not be the case! STORMED hybrid systems are introduced in this dissertation and form a subclass of hybrid automata which lie on the boundary of decidability and admit