Title:

DMOC: On its convergence, hierarchical approaches, and future directions

Abstract:

In order to solve optimal control problems for mechanical systems, the method "Discrete Mechanics and Optimal Control (DMOC)" links the theory of optimal control with concepts from variational mechanics. This talk places the discrete variational approach of DMOC within the context of optimal control theory and compares its strategy to existing solution methods.

Additionally, a convergence proof is described, i.e. solutions of the discrete optimal control problem converge to solutions of the continuous optimal control problem. The proof strategy bases on the computation of the consistency order of the discrete to the continuous necessary optimality conditions that are given by the Karush-Kuhn-Tucker equations and the Pontryagin maximum principle, respectively.

The second part of this talk focuses on different hierarchical approaches for the solution of optimal control problems to reduce the computational effort. The main ideas and some numerical results are presented.