## VDOL/spaceShuttleEntry_3

spaceShuttleEntry optimal control problem (matrix 3 of 4)
Name spaceShuttleEntry_3 VDOL 2732 1,834 1,834 28,757 28,757 Optimal Control Problem Yes 2015 B. Senses, A. Rao T. Davis
Structural Rank 1,834 true 1 1 0 100% 100% no no real
Download ```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/spaceShuttleEntry Space shuttle launch vehicle reentry optimal control problem is taken from Ref.~\cite{betts2010practical}. The goal of the optimal control problem is to determine the state and the control that maximize the cross range (maximize the final latitude) during the atmospheric entry of a reusable launch vehicle. State of the system is defined by the position, velocity, and the orientation of the space shuttle and the control of the system is the angle of attack and the bank angle of the space shuttle. The specified accuracy tolerance of \$10^{-8}\$ were satisfied after two mesh iterations. As the mesh refinement proceeds, the size of the KKT matrices increases from 560 to 2450.```