Qualitative simulation of continuous dynamic systems

This paper describes a constructive algorithm for performing the qualitative simulation of continuous dynamic systems. The algorithm may be thought of as the qualitative analogue of conventional numerical simulation. The equations of the system model are causally ordered to improve the efficiency of the algorithm; this also facilitates the production of causal explanations of system behaviour. We introduce the notion of 'differential planes' to allow the system model to be repeatedly differentiated. An additive input function is described by piecewise singularity functions and the algorithm includes the appropriate level of differential plane to remove the qualitative ambiguity. In this way the algorithm is able to cope with inputs as functions of time. We illustrate the application of the algorithm to a number of examples, and show that it overcomes some problems encountered with the non-constructive approach.