Extracting and Representing ualitative Behaviors of Cornplex Systerns 'in Phase Spaces
Abstract:
We develop a qualitative method for understanding and representing phase space structures of complex systems. To demonstrate this method, a program has been constructed that understands qualitatively different regions of the phase spaces and represents and extracts geometric shape information about these re-gions, using deep domain knowledge of dynamical system theory. Given a dynamical system specified as a system of governing equations, the program applies a successive sequence of operations to incrementally extract the qualitative information and generates a complete, high level symbolic descr ' tion of the phase space structure, through a combination of numerical, combinatorial, and geometric computations and-spatial reasoning techniques. The high level description is sensible to human beings and manipulable by other programs. We are currently applying the method to a dfficult engineering design domain in which controllers for complex systems are to be automatically synthesized to achieve desired properties, based on the knowledge of the "shapes " of the systems.
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