## VDOL/lowThrust_9

lowThrust optimal control problem (matrix 9 of 13)

Name | lowThrust_9 |
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Group | VDOL |

Matrix ID | 2713 |

Num Rows | 18,044 |

Num Cols | 18,044 |

Nonzeros | 219,589 |

Pattern Entries | 219,589 |

Kind | Optimal Control Problem |

Symmetric | Yes |

Date | 2015 |

Author | B. Senses, A. Rao |

Editor | T. Davis |

Download | MATLAB Rutherford Boeing Matrix Market |
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Notes |
Optimal control problem, Vehicle Dynamics & Optimization Lab, UF Anil Rao and Begum Senses, University of Florida http://vdol.mae.ufl.edu This matrix arises from an optimal control problem described below. Each optimal control problem gives rise to a sequence of matrices of different sizes when they are being solved inside GPOPS, an optimal control solver created by Anil Rao, Begum Senses, and others at in VDOL lab at the University of Florida. This is one of the matrices in one of these problems. The matrix is symmetric indefinite. Rao, Senses, and Davis have created a graph coarsening strategy that matches pairs of nodes. The mapping is given for this matrix, where map(i)=k means that node i in the original graph is mapped to node k in the smaller graph. map(i)=map(j)=k means that both nodes i and j are mapped to the same node k, and thus nodes i and j have been merged. This matrix consists of a set of nodes (rows/columns) and the names of these rows/cols are given Anil Rao, Begum Sense, and Tim Davis, 2015. VDOL/lowThrust Low-thrust orbit transfer optimal control problem is taken from Ref.~\cite{betts2010practical}. The goal of the low-thrust orbit transfer problem is to determine the state and the control that minimize the fuel consumption during the orbit transfer of a spacecraft that starts from a low-earth orbit and terminates at the geostationary orbit via low-thrust propulsion systems. The highly nonlinear dynamics of the low-thrust orbit transfer problem is given in modified equinoctial elements (state of the system) and the thrust direction (control of the system). Furthermore, the low-thrust optimal control problem is a badly scaled problem because of the small thrust-to-initial-mass ratio, that is typically on the order of $O(10^{-4})$, and the long orbit transfer duration. Badly scaling of the problem leads to a lot of delayed pivots. The specified accuracy tolerance of $10^{-8}$ were satisfied after thirteen mesh iterations. As the mesh refinement proceeds, the size of the KKT matrices increases from 584 to 18476. @book{betts2010practical, title={Practical Methods for Optimal Control and Estimation Using Nonlinear Programming}, author={Betts, John T}, volume={19}, year={2010}, publisher={SIAM Press}, address = {Philadelphia, Pennsylvania}, } |