The Theory of MUSCOD in a

MUSCOD (MU ltiple 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 Plitt81, Bock84]. 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 Bock84] 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 Plitt81], on the other hand, presents a fairly complete description, but is rather diicult to read. Throughout the present document, emphasis is given to a clear presentation of the concepts upon which MUSCOD is based. An eeort has been made to properly reeect 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.