Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Space

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. * The article describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology, supported in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N000l4-89-J-3202, and in part by the National Science Foundation grant MIP-90