VDOL/reorientation_3
reorientation optimal control problem (matrix 3 of 8)
Name 
reorientation_3 
Group 
VDOL 
Matrix ID 
2724 
Num Rows

2,513 
Num Cols

2,513 
Nonzeros

32,166 
Pattern Entries

32,166 
Kind

Optimal Control Problem 
Symmetric

Yes 
Date

2015 
Author

B. Senses, A. Rao 
Editor

T. Davis 
Structural Rank 
2,513 
Structural Rank Full 
true 
Num Dmperm Blocks

3 
Strongly Connect Components

2 
Num Explicit Zeros

0 
Pattern Symmetry

100% 
Numeric Symmetry

100% 
Cholesky Candidate

no 
Positive Definite

no 
Type

real 
Download 
MATLAB
Rutherford Boeing
Matrix Market

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/reorientation
Minimumtime reorientation of an asymmetric rigid body optimal
control problem is taken from Ref.~\cite{betts2010practical}. The
goal of the problem is to determine the state and the control that
minimize the time that is required to reorient a rigid body. The
state of the system is defined by quaternians that gives the
orientation of the spacecraft and the angular velocity of the
spacecraft and the control of the system is torque. The vehicle data
that is used to model the dynamics are taken from NASA Xray Timing
Explorer spacecraft. The specified accuracy tolerance of $10^{8}$
were satisfied after eight mesh iterations. As the mesh refinement
proceeds, the size of the KKT matrices increases from 677 to 3108.
@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},
}
