Author： Raisch J.
Publisher： Taylor & Francis Ltd
ISSN： 1387-3954
Source： Mathematical and Computer Modelling of Dynamical Systems, Vol.6, Iss.1, 2000-03, pp. : 6-29
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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 l ? ... ? 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.
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