Abstractions of hybrid systems: formal languages to describe dynamical behaviour ⋆

ions of hybrid systems: formal languages to describe dynamical behaviour ⋆ Rebekah Carter, Eva M. Navarro-López School of Computer Science, The University of Manchester Oxford Road, Manchester, M13 9PL, UK (e-mails: [email protected], [email protected]) Abstract: We show how finite-state automata over finite and infinite words can capture key dynamical properties of hybrid systems. The purpose is to obtain a discrete abstraction of the main complex dynamical behaviour patterns that such systems exhibit. We will form a labelled transition system as an abstraction of the hybrid system, and, in order to differentiate between the key dynamical behaviours, we will associate a set of formal languages to each of the behaviours. We will use both finite regular and infinite ω-regular languages. These formal languages can be accepted by a generalised Muller automaton, which is a novel approach in the specification of dynamical properties of hybrid systems. We show how finite-state automata over finite and infinite words can capture key dynamical properties of hybrid systems. The purpose is to obtain a discrete abstraction of the main complex dynamical behaviour patterns that such systems exhibit. We will form a labelled transition system as an abstraction of the hybrid system, and, in order to differentiate between the key dynamical behaviours, we will associate a set of formal languages to each of the behaviours. We will use both finite regular and infinite ω-regular languages. These formal languages can be accepted by a generalised Muller automaton, which is a novel approach in the specification of dynamical properties of hybrid systems.