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Chebyshev pseudospectral method
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<h2 id="other-chebyshev-methods">Other Chebyshev methods</h2> <p>The Chebyshev PS method is frequently confused with other Chebyshev methods. Prior to the advent of PS methods, many authors<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> proposed using <a href="/facts/Chebyshev_polynomials/HoBINqgC">Chebyshev polynomials</a> to solve <a href="/facts/Optimal_control/9SmcQHjJ">optimal control</a> problems; however, none of these methods belong to the class of <a href="/facts/Pseudospectral_method/62NCscTm">pseudospectral methods</a>. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Legendre_pseudospectral_method/XXJapl1u">Legendre pseudospectral method</a></li> <li><a href="/facts/Ross%25E2%2580%2593Fahroo_pseudospectral_method/4eYsAHNI">Ross–Fahroo pseudospectral methods</a></li> <li><a href="/facts/Ross%25E2%2580%2593Fahroo_lemma/nBox0YMD">Ross–Fahroo lemma</a></li> <li><a href="/facts/Bellman_pseudospectral_method/4yvQSXDg">Bellman pseudospectral method</a></li> <li><a href="/facts/DIDO_(optimal_control)/RkNUPMQd">DIDO</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Ross, I. M.; Karpenko, M. (2012). "A Review of Pseudospectral Optimal Control: From Theory to Flight". Annual Reviews in Control. 36 (2): 182–197. doi:10.1016/j.arcontrol.2012.09.002. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Elnagar, G.; Kazemi, M. A. (1998). "Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems". Computational Optimization and Applications. 11 (2): 195–217. doi:10.1023/A:1018694111831. S2CID 30241469. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Fahroo, F.; Ross, I. M. (2002). "Direct trajectory optimization by a Chebyshev pseudospectral method". Journal of Guidance, Control, and Dynamics. 25 (1): 160–166. Bibcode:2002JGCD...25..160F. doi:10.2514/2.4862. <a href="https://zenodo.org/record/1235943" target="_blank">https://zenodo.org/record/1235943</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Trefethen, Lloyd N. (2008). "Is Gauss quadrature better than Clenshaw–Curtis?". SIAM Review. 50 (1): 67–87. Bibcode:2008SIAMR..50...67T. CiteSeerX 10.1.1.468.1193. doi:10.1137/060659831. <a href="/wiki/Lloyd_N._Trefethen" target="_blank">/wiki/Lloyd_N._Trefethen</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Gong, Q.; Ross, I. M.; Fahroo, F. (2010). "Costate Computation by a Chebyshev Pseudospectral Method". Journal of Guidance, Control, and Dynamics. 33 (2): 623–628. Bibcode:2010JGCD...33..623G. doi:10.2514/1.45154. hdl:10945/48187. S2CID 55780038. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Q. Gong, I. M. Ross and F. Fahroo, A Chebyshev Pseudospectral Method for Nonlinear Constrained Optimal Control Problems, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, December 16–18, 2009 <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Vlassenbroeck, J.; Dooren, R. V. (1988). "A Chebyshev technique for solving nonlinear optimal control problems". IEEE Transactions on Automatic Control. 33 (4): 333–340. doi:10.1109/9.192187. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> </ol>