Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Spaces

Abstract

This paper presents a computational method for automatically analyzing qualitative behaviors of complex dynamical systems in phase space. To demonstrate this method, a program called MAPS has been constructed that understands qualitatively distinct features of a phase space and represents geometric information about these features in a dimension-independent description, using deep domain knowledge of dynamical systems theory. Given a dynamical system specified as a system of governing equations, MAPS incrementally extracts the qualitative information about the system in terms of a qualitative phase-space structure describing steady-state behaviors, stabilities, and transient properties. MAPS generates a high-level symbolic description of the system sensible to human beings and manipulable by other programs, through a combination of numerical, combinatorial, and geometric computations and spatial reasoning techniques. MAPS has successfully demonstrated its power in a difficult engineering domain of nonlinear control design.