| 翻訳と辞書 |
| Gauss pseudospectral method ： ウィキペディア英語版 |
Gauss pseudospectral method
The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program (NLP). The Gauss pseudospectral method differs from several other pseudospectral methods in that the dynamics are not collocated at either endpoint of the time interval. This collocation, in conjunction with the proper approximation to the costate, leads to a set of KKT 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.
==Description==
The method is based on the theory of orthogonal collocation where the collocation points (i.e., the points at which the optimal control problem is discretized) are the Legendre–Gauss (LG) points. The approach used in the GPM is to use a Lagrange polynomial approximation for the state that includes coefficients for the initial state plus the values of the state at the N LG points. In a somewhat opposite manner, the approximation for the costate (adjoint) is performed using a basis of Lagrange polynomials that includes the final value of the costate plus the costate at the N LG points. These two approximations together lead to the ability to map the KKT multipliers of the nonlinear program (NLP) to the costates of the optimal control problem at the N LG points PLUS the boundary points. The costate mapping theorem that arises from the GPM has been described in several references including two MIT PhD theses〔Benson, D.A., ''A Gauss Pseudospectral Transcription for Optimal Control'', Ph.D. Thesis, Dept. of Aeronautics and Astronautics, MIT, November 2004,〕〔Huntington, G.T., ''Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control'', Ph.D. Thesis, Dept. of Aeronautics and Astronautics, MIT, May 2007〕 and journal articles that include the theory along with applications〔Benson, D.A., Huntington, G.T., Thorvaldsen, T.P., and Rao, A.V., "Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method", ''Journal of Guidance, Control, and Dynamics''. Vol. 29, No. 6, November–December 2006, pp. 1435–1440.,〕〔Huntington, G.T., Benson, D.A., and Rao, A.V., "Optimal Configuration of Tetrahedral Spacecraft Formations", ''The Journal of The Astronautical Sciences''. Vol. 55, No. 2, March–April 2007, pp. 141–169.〕〔Huntington, G.T. and Rao, A.V., "Optimal Reconfiguration of Spacecraft Formations Using the Gauss Pseudospectral Method", ''Journal of Guidance, Control, and Dynamics''. Vol. 31, No. 3, March–April 2008, pp. 689–698.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Gauss pseudospectral method」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|