Higher Order Derivative Constraints in Qualitative Simulation

Qualitative simulation is a useful method for predicting the possible qualitatively distinct behaviors of an incompletely known mechanism described by a system of qualitative diierential equations (QDEs). Under some circumstances, sparse information about the derivatives of variables can lead to intractable branching (or \chatter") representing uninteresting or even spurious distinctions among qualitative behaviors. The problem of chatter stands in the way of real applications such as qualitative simulation of models in the design or diagnosis of engineered systems. One solution to this problem is to exploit information about higher-order derivatives of the variables. We demonstrate automatic methods for identiication of chattering variables, algebraic derivation of expressions for second-order derivatives, and evaluation and application of the sign of second-and third-order derivatives of variables, resulting in tractable simulation of important qualitative models. Caution is required, however, when deriving higher-order derivative (HOD) expressions from models including incompletely known mono-tonic function (M +) constraints, whose derivatives beyond the sign of the slope are completely unspeciied. We discuss the strengths and weaknesses of several methods for evaluating HOD expressions in this situation. We also discuss a second approach to intractable branching, in which we change the level of description to collapse an innnite set of distinct behaviors into a few by ignoring certain distinctions. These two approaches represent a trade-oo between generality and power. Each application of these methods can take a position on this trade-oo depending on its own critical needs.