%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/VDOL/spaceStation_13
% name: VDOL/spaceStation_13
% [spaceStation optimal control problem (matrix 13 of 14)]
% id: 2746
% date: 2015
% author: B. Senses, A. Rao
% ed: T. Davis
% fields: name title A b id date author ed kind notes aux
% aux: rowname mapping
% kind: optimal control problem
%-------------------------------------------------------------------------------
% 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/spaceStation                                                      
%                                                                        
% Space station attitude optimal control problem is taken from           
% Ref.~\cite{betts2010practical}. The goal of the space station          
% attitude control problem is to determine the state and the control     
% that minimize the magnitude of the final momentum while the space      
% statition reaches an orientation at the final time that can be         
% maintained without utilizing additional control torque. The state of   
% the system is defined by the angular velocity of the spacecraft with   
% respect to an inertial reference frame, Euler-Rodriguez parameters     
% used to defined the vehicle attitude, and the angular momentum of the  
% control moment gyroscope and the control of the system is the torque.  
% The specified accuracy tolerance of $10^{-7}$ were satisfied after     
% thirteen mesh iterations. As the mesh refinement proceeds, the size    
% of the KKT matrices increases from 99 to 1640.                         
%-------------------------------------------------------------------------------
