Matrix: VDOL/spaceStation_1

Description: spaceStation optimal control problem (matrix 1 of 14)

VDOL/spaceStation_1 graph
(undirected graph drawing)

VDOL/spaceStation_1 dmperm of VDOL/spaceStation_1
scc of VDOL/spaceStation_1

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  • download as a MATLAB mat-file, file size: 41 KB. Use UFget(2734) or UFget('VDOL/spaceStation_1') in MATLAB.
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    Matrix properties
    number of rows99
    number of columns99
    structural full rank?yes
    structural rank99
    # of blocks from dmperm7
    # strongly connected comp.3
    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 99-by-1
    rownamefull 99-by-97
    mappingfull 99-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.                            
    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.                         

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD1,188
    Cholesky flop count2.3e+04
    nnz(L+U), no partial pivoting, with AMD2,277
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,773
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD2,922

    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.