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 Schrodinger equation.
Pursuit strategies (formulated using constant-speed particle models) provide a means for achieving cohesive behavior in systems of multiple mobile agents. In the present paper, we explore an n-agent cyclic pursuit scheme (i.e. agent i pursues agent i+1, modulo n) in which each agent employs a constant bearing pursuit strategy. We demonstrate the existence of an invariant submanifold, and state necessary and sufficient conditions for the existence of rectilinear and circling ...
Reports by Author
