Gauss pseudospectral method

<p>The Gauss pseudospectral method (GPM), one of <a href="/facts/List_of_topics_named_after_Carl_Friedrich_Gauss/PcIz5lFw">many topics named after</a> <a href="/facts/Carl_Friedrich_Gauss/f4eSMBD7">Carl Friedrich Gauss</a>, is a direct transcription method for discretizing a continuous <a href="/facts/Optimal_control/9SmcQHjJ">optimal control</a> problem into a <a href="/facts/Nonlinear_programming/cSXGuX2m">nonlinear program</a>  (NLP). The Gauss pseudospectral method differs from several other <a href="/facts/Pseudospectral_optimal_control/Gv0XADRR">pseudospectral methods</a>  in that the dynamics are not collocated at either endpoint of the time interval.  This collocation, in conjunction with the proper approximation to the <a href="/facts/Costate/KgNTRV4h">costate</a>, leads to a set of <a href="/facts/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions/ly7g2zST">KKT</a> conditions that are identical to the discretized form of the first-order optimality conditions. This equivalence between the KKT conditions and the discretized first-order optimality conditions leads to an accurate costate estimate using the KKT multipliers of the NLP.
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Gauss pseudospectral method open-in-new

Gauss pseudospectral method