**Abstract.**
MUSCOD (MUltiple Shooting COde for Direct Optimal Control) is the
implementation of an algorithm for the direct solution of optimal
control problems. The method is based on multiple shooting combined
with a sequential quadratic programming (SQP) technique; its original
version was developed in the early 1980s by Plitt under the supervision
of Bock [1,2]. The following report is intended to describe the basic
aspects of the underlying theory in a concise but readable form. Such
a description is not yet available: the paper by Bock and Plitt [2]
gives a good overview of the method, but it leaves out too many
important details to be a complete reference, while the diploma thesis
by Plitt [1], on the other hand, presents a fairly complete
description, but is rather difficult to read. Throughout the present
document, emphasis is given to a clear presentation of the concepts
upon which MUSCOD is based. An effort has been made to properly reflect
the structure of the algorithm and to give a good motivation for its
fundamental parts. Of course, recent developments have been taken into
account, and it should be noted that some of the material presented
here has not been previously published. Proofs which are readily found
elsewhere have not been included. It is hoped that this tutorial
description will help new users of MUSCOD to quickly become familiar
with the necessary theory, and perhaps it will also be useful for
people who want to modify or extend the existing algorithm.

- Plitt, K.-J.: Ein superlinear konvergentes Mehrzielverfahren zur
direkten Berechnung beschränkter optimaler Steuerungen.
Diplomarbeit, Universität Bonn, 1981.

- Bock, H.G., and K.-J. Plitt: A multiple shooting algorithm for
direct solution of optimal control problems. Proceedings of the 9th
IFAC World Congress, Budapest. Pergamon Press, 1984.

Correspondence should be addressed to daniel.leineweber.dl@bayertechnology.com |