Pseudospectral Methods for Infinite-Horizon Optimal Control Problems
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Authors
Fahroo, Fahroo
Ross, Michael I.
Subjects
Advisors
Date of Issue
2008
Date
2008
Publisher
Language
en_US
Abstract
A central computational issue in solving infinite-horizon nonlinear optimal control problems is the treatment of the
horizon. In this paper, we directly address this issue by a domain transformation technique that maps the infinite
horizon to a finite horizon. The transformed finite horizon serves as the computational domain for an application of
pseudospectral methods. Although any pseudospectral method may be used, we focus on the Legendre
pseudospectral method. It is shown that the proper class of Legendre pseudospectral methods to solve infinitehorizon
problems are the Radau-based methods with weighted interpolants. This is in sharp contrast to the
unweighted pseudospectral techniques for optimal control. The Legendre–Gauss–Radau pseudospectral method is
thus developed to solve nonlinear constrained optimal control problems. An application of the covector mapping
principle for the Legendre–Gauss–Radau pseudospectral method generates a covector mapping theorem that
provides an efficient approach for the verification and validation of the extremality of the computed solution. Several
example problems are solved to illustrate the ideas.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.2514/1.33117
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
Secretary of the U.S. Air Force
Funding
U.S. Air Force Office of Scientific Research under
Grant F1ATA0-60-6-2G002
Format
11 p.
Citation
Fahroo, F. & Ross, I.M. 2008, "Pseudospectral methods for infinite-horizon optimal control problems", Journal of Guidance Control and Dynamics, vol. 31, no. 4, pp. 927-936.
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.