An Approach to Modelling and Simulation of Uncertain Dynamical Systems

Abstract

Coping with uncertainty in dynamical systems has recently received some attention in artificial intelligence (AI), particularly in the fields of qualitative and model-based reasoning. In this paper, we propose an approach to modelling and simulation of uncertain dynamics which is based on the following ideas: We consider (linguistic) descriptions of uncertain functional relationships characterizing the behavior of some dynamical system. Based on a certain interpretation of such rule-based models, we derive a fuzzy function [Formula: see text]. It will be shown that all (reasonable) fuzzy functions can be approximated to any degree of accuracy in this way. The function [Formula: see text] is then used as the "fuzzy" right hand side of a set of differential equations, which leads us to consider fuzzy initial value problems. We are going to propose an interpretation of such problems. Moreover, several aspects of simulation methods for characterizing the set of all system behaviors compatible with this interpretation will be discussed.