Spectral Algorithm for Pseudospectral Methods in Optimal Control
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Authors
Gong, Qi
Fahroo, Fahroo
Ross, Michael I.
Subjects
Advisors
Date of Issue
2008
Date
2008
Publisher
Language
en_US
Abstract
Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control problems. The concept of pseudospectral knots and Gaussian quadrature rules are used to
generate a natural spectral mesh that is dense near the points of interest. Several stopping criteria are developed based on new error-estimation formulas and Jackson’s theorem. The sequence is terminated when all of the convergence criteria are satisfied. Numerical examples demonstrate the key concepts proposed in the design of the spectral algorithm. Although a vast number of theoretical and algorithmic issues still remain open, this paper
advances pseudospectral methods along several new directions and outlines the current theoretical pitfalls in computation and control.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.2514/1.32908
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
U.S. Air Force Office of Scientific Research
Secretary of the U.S. Air Force
Naval Postgraduate School
NASA
Secretary of the U.S. Air Force
Naval Postgraduate School
NASA
Funder
Naval Postgraduate School Grant N00244-07-1-0008.
U.S. Air Force Office of Scientific Research under grant F1ATA0-60-6-2G002.
U.S. Air Force Office of Scientific Research under grant F1ATA0-60-6-2G002.
Format
13 p.
Citation
Gong, Q., Fahroo, F. & Ross, I.M. 2008, "Spectral algorithm for pseudospectral methods in optimal control", Journal of Guidance Control and Dynamics, vol. 31, no. 3, pp. 460-471.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.