Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 352, Issue 10, Pages 4081-4106Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2015.05.028
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Funding
- U.S. Office of Naval Research [N00014-11-1-0068, N00014-15-1-2048]
- U.S. Defense Advanced Research Projects Agency [HR0011-12-C-0011]
- U.S. National Science Foundation [CBET-1404767]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1522629] Funding Source: National Science Foundation
- Div Of Chem, Bioeng, Env, & Transp Sys
- Directorate For Engineering [1404767] Funding Source: National Science Foundation
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An adaptive mesh refinement method for solving optimal control problems is developed. The method employs orthogonal collocation at Legendre-Gauss-Radau points, and adjusts both the mesh size and the degree of the approximating polynomials in the refinement process. A previously derived convergence rate is used to guide the refinement process. The method brackets discontinuities and improves solution accuracy by checking for large increases in higher-order derivatives of the state. In regions between discontinuities, where the solution is smooth, the error in the approximation is reduced by increasing the degree of the approximating polynomial. On mesh intervals where the error tolerance has been met, mesh density may be reduced either by merging adjacent mesh intervals or lowering the degree of the approximating polynomial. Finally, the method is demonstrated on two examples from the open literature and its performance is compared against a previously developed adaptive method. (C) 2015 The Franldin Institute. Published by Elsevier Ltd. on behalf of The Franldin Institute.
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