Communications in Information and Systems

Volume 11 (2011)

Number 1

Optimal natural frames

Pages: 17 – 34

DOI: http://dx.doi.org/10.4310/CIS.2011.v11.n1.a2

Authors

Eric W. Justh (Naval Research Laboratory, Washington, DC)

P.S. Krishnaprasad (Institute for Systems Research, University of Maryland, College Park)

Abstract

Problems of optimal control on Lie groups are of broad interest and application dating back to the early days of geometric control theory. We study a class of such problems defined on the special Euclidean group and demonstrate by appealing to reduction methods that the extremals in these problems admit special structure associated to the nonlinear Schrödinger equation.

Keywords

natural frames, optimal control on Lie groups, Lie-Poisson reduction, nonlinear Schrödinger equation, vortex filament

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