Qualitative Euler Integration with Continuity

J. Allan Scott and George M. Coghill

The subject of this paper is a novel synchronous fuzzy qualitative simulator developed within the Mycroft fuzzy qualitative reasoning framework. Synchronous fuzzy qualitative simulation involves replacing the transition rules of Mycroft with an integration phase utilising a qualitative version of Eulers first order approximation to the Taylor series: Qualitative Euler Integration (QEI). The simulation process described utilises constraint-based fuzzy qualitative models, the variables of which take their values from a predefined fuzzy quantity space. The simulation proceeds, driven by an externally defined integration time step (chosen to ensure the continuity of the magnitudes of the state variables), by means of an explicit Euler integration operation. This provides the set of possible successor values for the magnitudes of the state variables. After this the constraints of the model are solved to provide the values of the non-state variables of the model. As each constraint is solved the same transition rules as for asynchronous simulation are applied to constrain the generation of the behaviour tree. At the end of this process a number of successor states will be generated This number will be less than or equal to the number generated by semi-constructive or non-constructive simulators such as Mycroft or FuSim, and a great deal less than if the transition filters had not been applied. The advantage of this approach is that it permits the utilisation of multiple precision models in which the information concerning the values of system variables may be expressed in vague terms but with precise time stamp information. The system has already been utilised in a research exploring the use of qualitative models for parameter identification, diagnosis and control.

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