Matrix: VDOL/dynamicSoaringProblem_2

Description: dynamicSoaringProblem optimal control problem (matrix 2 of 8)

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  • download as a MATLAB mat-file, file size: 140 KB. Use UFget(2666) or UFget('VDOL/dynamicSoaringProblem_2') in MATLAB.
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    Matrix properties
    number of rows1,591
    number of columns1,591
    structural full rank?yes
    structural rank1,591
    # 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 1591-by-1
    rownamefull 1591-by-99
    mappingfull 1591-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.                            
    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.                                                     
      title={Optimal Patterns of Glider Dynamic Soaring},                  
      author={Zhao, Yiyuan J},                                             
      journal={Optimal Control applications and methods},                  
      publisher={Wiley Online Library}                                     

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD26,621
    Cholesky flop count7.6e+05
    nnz(L+U), no partial pivoting, with AMD51,651
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD232,303
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD399,373

    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.