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ANZIAM J. 47(EMAC2005) pp.C101--C115, 2006.

A Gauss--Lobatto quadrature method for solving optimal control problems

P. Williams

(Received 29 August 2005; revised 13 July 2006)

Abstract

This paper proposes a direct approach for solving optimal control problems. The time domain is divided into multiple subdomains, and a Lagrange interpolating polynomial using the Legendre--Gauss--Lobatto points is used to approximate the states and controls. The state equations are enforced at the Legendre--Gauss--Lobatto nodes in a nonlinear programming implementation by partial Gauss--Lobatto quadrature in each subdomain. The final state in each subdomain is enforced by a full Gauss--Lobatto quadrature. The Bolza cost functional is naturally approximated using Gauss--Lobatto quadrature across all subdomains.

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Authors

P. Williams

School of Aerospace, Mechanical, and Manufacturing Engineering, RMIT University, Bundoora, Australia. mailto:paul.williams@rmit.edu.au

Published July 24, 2006. ISSN 1446-8735

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