Piecewise Linear Reasoning

Elisha Sacks

This paper describes a new technique called piecewise linear reasoning (PLR) for analyzing dynamic systems describable by finite sets of ordinary differential equations. Current qualitative reasoning programs derive the abstract behavior of a system by simulating handcrafted "qualitative" versions of the differential equations that characterize it and summarizing the results. PLR infers more detailed information by constructing and examining piecewise linear approximations of the original equations. As evidence that PLR can provide useful information to engineers, its analyses of the Lienard and van der Pol equations are presented.

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