## VDOL/orbitRaising_1

orbitRaising optimal control problem (matrix 1 of 4)
Name orbitRaising_1 VDOL 2718 442 442 2,906 2,906 Optimal Control Problem Yes 2015 B. Senses, A. Rao T. Davis
Structural Rank 442 true 3 2 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/orbitRaising Orbit raising problem that is taken from Ref.~\cite{bryson1975applied}. The goal of the optimal control problem is to determine the state and the control that maximize the radius of an orbit transfer in a given time. The state of the system is defined by radial distance of the spacecraft from the attracting center (e.g Earth, Mars, etc.) and velocity of the spacecraft and the control is the thrust direction. The specified accuracy tolerance of \$10^{-8}\$ were satisfied after four mesh iterations. As the mesh refinement proceeds, the size of the KKT matrices increases from 442 to 915. @book{bryson1975applied, title={Applied Optimal Control: Optimization, Estimation, and Control}, author={Bryson, Arthur Earl}, year={1975}, publisher={CRC Press} }```