Communications in Information and Systems
Volume 11 (2011)
Optimal natural frames
Pages: 17 – 34
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.
natural frames, optimal control on Lie groups, Lie-Poisson reduction, nonlinear Schrödinger equation, vortex filament