On consistent symbolic representations of general dynamic systems

This paper deals with the issue of consistent symbolic (qualitative) representation of continuous dynamic systems. Consistency means here that the results of reasoning with the qualitative representation hold in the underlying (quantitative) dynamic system. In the formalization proposed in this paper, the quantitative structure is represented using the notion of a general dynamic system (GDS). The qualitative counterpart (QDS), is represented by a finite-state automaton structure. The two representational substructures are related through functions, called qualitative abstractions of dynamic systems. Qualitative abstractions associate inputs, states and outputs of the QDS, with partitions of appropriate GDS spaces. The paper shows how to establish such consistent partitions, given a partitioning of the system´s output. To represent borders of these partitions, the notion of critical hypersurfaces is introduced. One of the main ideas that provides consistency is the interpretation of qualitative input events as elements of the partition of the Cartesian product of input, initial state and time sets. An example of a consistent qualitative/quantitative representation of a simple dynamic system, and of reasoning using such a representation, is provided