# Category:Muscod

This category lists all problems that have a description of differential equations in MUSCOD-format.

MUSCOD is an abbreviation for MUltiple Shooting COde for Direct Optimal Control. The original version was developed by Bock and Plitt in the 1980s and used in the seminal paper [Bock1984]**Address: ** *Budapest***Author: ** *H.G. Bock; K.J. Plitt***Booktitle: ** *Proceedings of the 9th IFAC World Congress***Pages: ** *242--247***Publisher: ** *Pergamon Press***Title: ** *A Multiple Shooting algorithm for direct solution of optimal control problems***Url: ** *http://www.iwr.uni-heidelberg.de/groups/agbock/FILES/Bock1984.pdf***Year: ** *1984*

which is often cited as the origin of the Direct Multiple Shooting method. The reimplementation MUSCOD-II by Daniel Leineweber in the 1990s is still the basis for ongoing development, in particular in the work groups of Georg Bock, Christian Kirches, Andreas Potschka (all Heidelberg), and Sebastian Sager (Magdeburg). MUSCOD-II is based on the direct multiple shooting method to treat multistage optimal control problems with DAE constraints. The extension MS-MINTOC by Sager is able to treat integrality requirements in an efficient way, compare [Sager2009]**Author: ** *Sager, S.; Reinelt, G.; Bock, H.G.***Journal: ** *Mathematical Programming***Number: ** *1***Pages: ** *109--149***Title: ** *Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems***Url: ** *http://mathopt.de/PUBLICATIONS/Sager2009.pdf***Volume: ** *118***Year: ** *2009*

.

For a standard MIOC written as

the format looks, e.g., something like this:

rhs[0] = xd[0] - xd[0]*xd[1] - p[0]*u[0]*xd[0]; rhs[1] = - xd[1] + xd[0]*xd[1] - p[1]*u[0]*xd[1];

for the special case

Here the vector entries *rhs[i]* contain the values of the right hand side function . The vector entries *xd[i]* contains the differential variables , *u[i]* the control variables or , and *p[i]* contains the model parameters or control differential variables resp. .

## References

[Bock1984] | H.G. Bock; K.J. Plitt (1984): A Multiple Shooting algorithm for direct solution of optimal control problems. Pergamon Press, Proceedings of the 9th IFAC World Congress | |

[Sager2009] | Sager, S.; Reinelt, G.; Bock, H.G. (2009): Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems. Mathematical Programming, 118, 109--149 |

## Pages in category "Muscod"

The following 9 pages are in this category, out of 9 total.