Matrix: VDOL/hangGlider_2

Description: hangGlider optimal control problem (matrix 2 of 5)

VDOL/hangGlider_2 graph
(undirected graph drawing)


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  • Matrix group: VDOL
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  • download as a MATLAB mat-file, file size: 138 KB. Use UFget(2692) or UFget('VDOL/hangGlider_2') in MATLAB.
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    Matrix properties
    number of rows1,647
    number of columns1,647
    structural full rank?yes
    structural rank1,647
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorB. Senses, A. Rao
    editorT. Davis
    kindoptimal control problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 1647-by-1
    rownamefull 1647-by-80
    mappingfull 1647-by-1


    Optimal control problem, Vehicle Dynamics & Optimization Lab, UF       
    Anil Rao and Begum Senses, University of Florida                                                                  
    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.                            
    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     
      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},                                                

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD14,847
    Cholesky flop count1.5e+05
    nnz(L+U), no partial pivoting, with AMD28,047
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD182,425
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,115,954

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 04-Jun-2015.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.