Discrete Abstractions of Continuous Systems – an Input/Output Point of View

Abstract

This contribution proposes a hierarchy of discrete ions for a given continuous model. It adopts an input/output point of view, and starts from the continuous system behaviour B _c (i.e., 'the set of all pairs of input and output signals which are compatible with the continuous model equations). The first step is to construct a sequence of behaviours B _l , l =0, 1,..., such that B ₀ ⊇ B ₁ ⊇... ⊇ B _c. In a second step, nondeterministic Moore automata A_l are generated as minimal realizations for the behaviours B _l . Hence, the continuous base system and its discrete abstractions A l form a totally ordered set of models, where ordering is in the sense of set inclusion of model behaviours or, equivalently, in terms of approximation accuracy. Within this set, there exists a uniquely defined “coarsest” (and therefore least complex) model which allows a given set of specifications to be enforced by discrete feedback. The ordering property implies that this discrete feedback also forces the continuous base system to obey the specifications.