DISCRETE MECHANICS AND OPTIMAL CONTROL: AN ANALYSIS ∗

By Sina Ober-Blöbaum, Oliver Junge, Jerrold E. Marsden. 2008

206 citations recorded by the source corpus.

The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper is to directly discretize the variational description of the system's motion. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. We show that the DMOC (Discrete Mechanics and Optimal Control) approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The numerical performance of DMOC and its relationship to other existing optimal control methods are investigated.

Subfields: Computational Mechanics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ca86ebbce2064371db9a3249c5ddcc9cae2c119b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Francesco dell'Isola
2. Sigrid Leyendecker
3. A. Della Corte

In Control and Systems Engineering

1. Francesco dell'Isola
2. David J. Steigmann
3. Ramona Hoffmann
4. Gabriele Bleser
5. Markus Miezal
6. Sigrid Leyendecker
7. Tobias Gail
8. Ivan Giorgio

In Numerical Analysis

1. Ramona Hoffmann
2. Gabriele Bleser
3. Markus Miezal
4. Sigrid Leyendecker
5. Tobias Gail

Citations in the corpus

• Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response (2015, background): “(1) Capturing all the important features of a given discrete system [234].”
• Towards bridging the gap between motion capturing and biomechanical optimal control simulations (2015, methodology): “In this work, a direct transcription method called discrete mechanics and optimal control for constrained systems (DMOCC), see [11, 14], falling into the latter class, is used to approximate the solution at the time nodes t0, t1 = t0 + h, .”