Variational Principles and Control of Collective Behavior
P. S. Krishnaprasad (March 18, 2011)
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Geometric methods in control theory have had a useful role in the investigation of dynamics of collectives. In this talk, we build on models from this theory to sketch recent progress in understanding small networks governed by interaction strategies associated with pursuit. We extend these ideas to a broader array of variational principles in networks of interacting systems. Using symmetry and reduction methods, hamiltonian structures, and conservation laws, we explore questions of collective behavior. These results also suggest how such principles may be exploited in the extraction of individual behaviors from movement data on flocks and swarms.