Conservation of Generalized Momentum Maps in the Optimal Control of Constrained Mechanical Systems

摘要

We show that the optimal control of constrained mechanical systems satisfies an optimal control version of Noether’s theorem. In particular, the symmetry of the uncontrolled mechanical system subject to algebraic constraints is handed down to the optimal control problem. We also show that the corresponding generalized momentum map on the level of the optimal control problem can be preserved under discretization.