Higher-order derivative constraints in qualitative simulation
We demonstrate automatic methods for identification 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 monotonic functions \((M^ +)\) constraints, whose derivatives beyond the sign of the slope are completely unspecified. 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 infinite set of distinct behaviors into a few by ignoring certain distinctions. These two approaches represent a tradeoff between generality and power. Each application of these methods can take a position on this tradeoff depending on its own critical needs.
scientific article; zbMATH DE number 55599