VDOL/orbitRaising_1
orbitRaising optimal control problem (matrix 1 of 4)
Name 
orbitRaising_1 
Group 
VDOL 
Matrix ID 
2718 
Num Rows

442 
Num Cols

442 
Nonzeros

2,906 
Pattern Entries

2,906 
Kind

Optimal Control Problem 
Symmetric

Yes 
Date

2015 
Author

B. Senses, A. Rao 
Editor

T. Davis 
Structural Rank 
442 
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/orbitRaising
Orbit raising problem that is taken from
Ref.~\cite{bryson1975applied}. The goal of the optimal control
problem is to determine the state and the control that maximize the
radius of an orbit transfer in a given time. The state of the system
is defined by radial distance of the spacecraft from the attracting
center (e.g Earth, Mars, etc.) and velocity of the spacecraft and the
control is the thrust direction. The specified accuracy tolerance of
$10^{8}$ were satisfied after four mesh iterations. As the mesh
refinement proceeds, the size of the KKT matrices increases from 442
to 915.
@book{bryson1975applied,
title={Applied Optimal Control: Optimization, Estimation, and
Control},
author={Bryson, Arthur Earl},
year={1975},
publisher={CRC Press}
}
