A Gauss–Lobatto quadrature method for solving optimal control problems
نویسنده
چکیده
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. ∗School of Aerospace, Mechanical, and Manufacturing Engineering, RMIT University, Bundoora, Australia. mailto:[email protected] See http://anziamj.austms.org.au/V47EMAC2005/Williams2 for this article, c © Austral. Mathematical Soc. 2006. Published July 24, 2006. ISSN 1446-8735 ANZIAM J. 47 (EMAC2005) pp.C101–C115, 2006 C102
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