%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/VDOL/hangGlider_3
% name: VDOL/hangGlider_3
% [hangGlider optimal control problem (matrix 3 of 5)]
% id: 2693
% 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/hangGlider                                                        
%                                                                        
% Range maximization of a hang glider optimal control problem is taken   
% from Ref.~\cite{bulirsch1993combining}.  The goal of the optimal       
% control problem is to determine the state and the control that         
% maximize the range of the hang glider in the presence of a thermal     
% updraft. The state of the system is defined by horizontal distance,    
% altitude, horizontal velocity, and the vertical velocity and the       
% control is the lift coefficient. The specified accuracy tolerance of   
% $10^{-8}$ were satisfied after five mesh iterations. As the mesh       
% refinement proceeds, the size of the KKT matrices increases from 360   
% to 16011. This problem is sensitive to accuracy of the mesh and it     
% requires excessive number of collocation points to be able to satisfy  
% the accuracy tolerance. Thus, the size of the KKT matrices changes     
% drastically.                                                           
%                                                                        
% @book{bulirsch1993combining,                                           
%   title={Combining Direct and Indirect Methods in Optimal Control:     
%      Range Maximization of a Hang Glider},                             
%   author={Bulirsch, Roland and Nerz, Edda and Pesch, Hans Josef and    
%      von Stryk, Oskar},                                                
%   year={1993},                                                         
%   publisher={Springer}                                                 
% }                                                                      
%-------------------------------------------------------------------------------
