%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/VDOL/dynamicSoaringProblem_7
% name: VDOL/dynamicSoaringProblem_7
% [dynamicSoaringProblem optimal control problem (matrix 7 of 8)]
% id: 2671
% 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/dynamicSoaring                                                    
%                                                                        
% Dynamic soaring optimal control problem is taken from                  
% Ref.~\cite{zhao2004optimal} where the dynamics of a glider is          
% derived using a point mass model under the assumption of a flat        
% Earth and stationary winds. The goal of the dynamic soaring            
% problem is to determine the state and the control that minimize        
% the average wind gradient slope that can sustain a powerless           
% dynamic soaring flight.  The state of the system is defined by the     
% air speed, heading angle, air-realtive flight path angle,              
% altitude, and the position of the glider and the control of the        
% system is the lift coefficient. The specified accuracy tolerance       
% of $10^{-7}$ were satisfied after eight mesh iterations. As the        
% mesh refinement proceeds, the size of the KKT matrices increases       
% from  647 to 3543.                                                     
%                                                                        
% @article{zhao2004optimal,                                              
%   title={Optimal Patterns of Glider Dynamic Soaring},                  
%   author={Zhao, Yiyuan J},                                             
%   journal={Optimal Control applications and methods},                  
%   volume={25},                                                         
%   number={2},                                                          
%   pages={67--89},                                                      
%   year={2004},                                                         
%   publisher={Wiley Online Library}                                     
% }                                                                      
%-------------------------------------------------------------------------------
