Tuesday, May 11, 1999
4:00 PM (reception following)
Room 35-225
LIDS Colloquium
Abstract
Beginning with ignorable coordinates of Lagrange, there is a long history of symmetry principles and geometrical ideas playing a key role in our understanding of model reduction. In modern developments, methods of symplectic reduction have found their way into areas of mathematics beyond the original context of mechanics. It is however difficult to see how these developments fit into the input-output (or behavioral) framework of system theory, in part due to the requirements of _strict_ symmetries.
The task of producing reduced order models from complex models has a moderately long history in statistical analysis and in control theory under various names such as principal component analysis (PCA), Karhunen-Loeve decomposition, balancing etc. One needs to work with _approximate_ symmetries in some sense. In the setting of nonlinear systems the techniques are less well-developed, in part due to a lack of effective algorithms for determining the necessary ignorable coordinates. In this talk we will present some techniques for finding such coordinates, provide stochastic formulations of the nonlinear balancing problem, and discuss some motivating examples (e.g. semiconductor process models). This is in part joint work with A. J. Newman.
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Modified: May 12, 1999|
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