An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials

Albert L. Herman, Bruce A. Conway

Research output: Contribution to conferencePaper

Abstract

A new strategy for automating the node placement in an optimal control problem, solved using third-order Herrnite polynomials to model the state time histories, is discussed. This Hermite polynomial results in an approximate solution to the system differential equations by taking on the form of the Simpson’s quadrature rule. The automatic node placement strategy uses an error function based on an adaptive quadrature method for Simpson's rule. The method compares solutions generated using two successive nodal distributions to determine how to refine a nodal distribution. The algorithm is applied to a continuously thrusting spacecraft trajectory problem where the final energy of the trajectory is maximized for a fixed final time. The use of this automatic node placement algorithm yields a more accurate solution than that obtained with an equal number of evenly spaced nodes.

Original languageEnglish (US)
Pages270-280
Number of pages11
StatePublished - Jan 1 1992
EventAstrodynamics Conference, 1992 - Hilton Head Island, United States
Duration: Aug 10 1992Aug 12 1992

Other

OtherAstrodynamics Conference, 1992
CountryUnited States
CityHilton Head Island
Period8/10/928/12/92

Fingerprint

optimal control
quadratures
polynomials
spacecraft trajectories
error functions
differential equations
trajectories
histories
energy

ASJC Scopus subject areas

  • Astronomy and Astrophysics

Cite this

Herman, A. L., & Conway, B. A. (1992). An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials. 270-280. Paper presented at Astrodynamics Conference, 1992, Hilton Head Island, United States.

An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials. / Herman, Albert L.; Conway, Bruce A.

1992. 270-280 Paper presented at Astrodynamics Conference, 1992, Hilton Head Island, United States.

Research output: Contribution to conferencePaper

Herman, AL & Conway, BA 1992, 'An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials', Paper presented at Astrodynamics Conference, 1992, Hilton Head Island, United States, 8/10/92 - 8/12/92 pp. 270-280.
Herman AL, Conway BA. An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials. 1992. Paper presented at Astrodynamics Conference, 1992, Hilton Head Island, United States.
Herman, Albert L. ; Conway, Bruce A. / An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials. Paper presented at Astrodynamics Conference, 1992, Hilton Head Island, United States.11 p.
@conference{e44f34e5dab84ffc8344d13cf612cf44,
title = "An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials",
abstract = "A new strategy for automating the node placement in an optimal control problem, solved using third-order Herrnite polynomials to model the state time histories, is discussed. This Hermite polynomial results in an approximate solution to the system differential equations by taking on the form of the Simpson’s quadrature rule. The automatic node placement strategy uses an error function based on an adaptive quadrature method for Simpson's rule. The method compares solutions generated using two successive nodal distributions to determine how to refine a nodal distribution. The algorithm is applied to a continuously thrusting spacecraft trajectory problem where the final energy of the trajectory is maximized for a fixed final time. The use of this automatic node placement algorithm yields a more accurate solution than that obtained with an equal number of evenly spaced nodes.",
author = "Herman, {Albert L.} and Conway, {Bruce A.}",
year = "1992",
month = "1",
day = "1",
language = "English (US)",
pages = "270--280",
note = "Astrodynamics Conference, 1992 ; Conference date: 10-08-1992 Through 12-08-1992",

}

TY - CONF

T1 - An automatic node placement strategy for optimal control problems discretized using third-degree Hermite polynomials

AU - Herman, Albert L.

AU - Conway, Bruce A.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - A new strategy for automating the node placement in an optimal control problem, solved using third-order Herrnite polynomials to model the state time histories, is discussed. This Hermite polynomial results in an approximate solution to the system differential equations by taking on the form of the Simpson’s quadrature rule. The automatic node placement strategy uses an error function based on an adaptive quadrature method for Simpson's rule. The method compares solutions generated using two successive nodal distributions to determine how to refine a nodal distribution. The algorithm is applied to a continuously thrusting spacecraft trajectory problem where the final energy of the trajectory is maximized for a fixed final time. The use of this automatic node placement algorithm yields a more accurate solution than that obtained with an equal number of evenly spaced nodes.

AB - A new strategy for automating the node placement in an optimal control problem, solved using third-order Herrnite polynomials to model the state time histories, is discussed. This Hermite polynomial results in an approximate solution to the system differential equations by taking on the form of the Simpson’s quadrature rule. The automatic node placement strategy uses an error function based on an adaptive quadrature method for Simpson's rule. The method compares solutions generated using two successive nodal distributions to determine how to refine a nodal distribution. The algorithm is applied to a continuously thrusting spacecraft trajectory problem where the final energy of the trajectory is maximized for a fixed final time. The use of this automatic node placement algorithm yields a more accurate solution than that obtained with an equal number of evenly spaced nodes.

UR - http://www.scopus.com/inward/record.url?scp=85007237352&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007237352&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85007237352

SP - 270

EP - 280

ER -