Perturbation Analysis with Qualitative Models

Abstract

Perturbation analysis deals with the relationships between small changes in a system's inputs or model and changes in its outputs. Reverse simulation is of particular interest, determining how to achieve desired outputs by perturbing inputs or model parameters. Some applications of this type of analysis are suggested. Perturbation analysis is developed in the context of continuous systems whose dynamics, over small ranges of the system's behaviour, can be represented by linear models. All variables and signals are represented by intervals with qualitative end points. Qualitative linear models are introduced to represent time-varying systems. These representations permit the use of network consistency algorithms to solve perturbation analysis problems. This paper is dedicated to the memory of Dr. Murdoch McKinnon, late of CAE Electronics Ltd. and Concordia University, who faithfully supported this research since its beginning.