Discrete mechanics and optimal control: An analysis

Finding a solution to optimal control problems for mechanical systems is of paramount importance in a number of applications, ranging from vehicle dynamics to bio-engineering. More precisely, in most cases real systems can be attacked only by feasible computational approaches. When dealing with a continuous model, there are many different possible patterns to reach a discrete algorithm. This paper focuses on the idea that discretization should be introduced at the very first stage, producing a new approach called Discrete Mechanics and Optimal Control. The latter has various advantages, in particular the discrete solution inherits structural properties, like symmetries and integrals of the motion, and may be convenient from computational point of view. The authors present the whole approach from theoretical properties all the way to simulations. They also add a very nice and honest conclusion section, where they point out the difficulty in finding global optima and some recipe to deal with that.

Benedetto Piccoli, Corresponding Editor

Discrete mechanics and optimal control: An analysis
Sina Ober-Blöbaum, Oliver Junge and Jerrold E. Marsden
ESAIM: COCV 17 (2011) 322-352