Matrix: VDOL/reorientation_3

Description: reorientation optimal control problem (matrix 3 of 8)

 (undirected graph drawing)

• Matrix group: VDOL
• download as a MATLAB mat-file, file size: 240 KB. Use UFget(2724) or UFget('VDOL/reorientation_3') in MATLAB.

 Matrix properties number of rows 2,513 number of columns 2,513 nonzeros 32,166 structural full rank? yes structural rank 2,513 # of blocks from dmperm 3 # strongly connected comp. 2 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? no positive definite? no

 author B. Senses, A. Rao editor T. Davis date 2015 kind optimal control problem 2D/3D problem? no

 Additional fields size and type b full 2513-by-1 rowname full 2513-by-81 mapping full 2513-by-1

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

Minimum-time 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 X-ray 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},