Ross–Fahroo拟谱法
Ross–Fahroo拟谱法（Ross–Fahroo pseudospectral methods）是由I. Michael Ross和Fariba Fahroo导入的方法，属于拟谱最佳控制中的一部份[1][2][3][4][5][6][7][8][9]。Ross–Fahroo拟谱法的例子有拟谱knotting法、平坦拟谱法、Legendre-Gauss-Radau拟谱法[10][11]以及无限时域滚动最佳控制的拟谱法[12] [13]。
简介
[编辑]Ross–Fahroo拟谱法是以位移过的高斯拟谱节点为基础，位移是靠线性变换或是非线性变换，高斯拟谱点是由Gauss-Lobatto或Gauss-Radau分布，从勒让德多项式或切比雪夫多项式而来。Gauss-Lobatto拟谱点可以用在有限时域滚动的最优控制问题，而Gauss-Radau拟谱点可以用在无限时域滚动的最优控制问题[14]。
数学应用
[编辑]Ross–Fahroo拟谱法可以由Ross–Fahroo引理求得，可以应用在统御方程是微分方程、微分几何方程、微分包含式的系统，及微分flat系统的。在经过简单的定义域变换后，也可以应用在无限时域滚动的最优控制问题[12] [13]。Ross–Fahroo拟谱法也是贝尔曼拟谱法的基础。
飞航应用及奖项
[编辑]TRoss–Fahroo拟谱法已用在全世界的许多实验室及实务应用中。NASA在2006年时用Ross–Fahroo拟谱法实现了国际空间站的零燃料机动（zero propellant maneuver）降落[15]。为了表彰这些进步的成果，AIAA将2010年飞行力学和控制奖（2010 Mechanics and Control of Flight Award）颁给Ross及Fahroo，原因是“改变飞行力学的现状”。Ross也获选为美国太空学会（AAS）的Fellow，原因是“在拟谱最佳控制中开创性的贡献。”
特点
[编辑]Ross–Fahroo拟谱法有一个重大特点，和以往强调“直接法”或“间接法”的其他方式不同。透过 Ross 及 Fahroo结合了相关定理[5][6][8][16]，证明了可以设计在“直接法”及“间接法”上都等效的拟谱最佳控制法。因此设计者可以直接用他们设计的方法为“直接法”，同时自动产生一个准确的对偶问题，为“间接法”。这种革命性的作法让Ross–Fahroo拟谱法广为使用[17]。
软体应用
[编辑]Ross–Fahroo拟谱法已实现在MATLAB的最佳控制求解器DIDO。
相关条目
[编辑]- 贝尔曼拟谱法
- DIDO，得名自迦太基女王狄多（Dido）
- 罗斯π引理
- Ross–Fahroo引理
参考资料
[编辑]- ^ N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorithms Boost Satellite Performance on the Cheap", IEEE综览, November 2012.
- ^ Jr-; Li, S; Ruths, J.; Yu, T-Y; Arthanari, H.; Wagner, G. Optimal Pulse Design in Quantum Control: A Unified Computational Method. Proceedings of the National Academy of Sciences. 2011, 108 (5): 1879–1884. PMC 3033291
. PMID 21245345. doi:10.1073/pnas.1009797108.
- ^ Kang, W. Rate of Convergence for the Legendre Pseudospectral Optimal Control of Feedback Linearizable Systems. Journal of Control Theory and Application. 2010, 8 (4): 391–405. doi:10.1007/s11768-010-9104-0.
- ^ Conway, B. A. A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems. Journal of Optimization Theory Applications. 2012, 152 (2): 271–306. doi:10.1007/s10957-011-9918-z.
- ^ 5.0 5.1 I. M. Ross and F. Fahroo, A Pseudospectral Transformation of the Covectors of Optimal Control Systems, Proceedings of the First IFAC Symposium on System Structure and Control, Prague, Czech Republic, 29–31 August 2001.
- ^ 6.0 6.1 I. M. Ross and F. Fahroo, Legendre Pseudospectral Approximations of Optimal Control Problems, Lecture Notes in Control and Information Sciences, Vol. 295, Springer-Verlag, 2003.
- ^ Ross, I. M.; Fahroo, F. Pseudospectral Knotting Methods for Solving Optimal Control Problems. Journal of Guidance, Control and Dynamics. 2004, 27 (3): 397–405. doi:10.2514/1.3426.
- ^ 8.0 8.1 I. M. Ross and F. Fahroo, Discrete Verification of Necessary Conditions for Switched Nonlinear Optimal Control Systems, Proceedings of the American Control Conference, Invited Paper, June 2004, Boston, MA.
- ^ Ross, I. M.; Fahroo, F. Pseudospectral Methods for the Optimal Motion Planning of Differentially Flat Systems. IEEE Transactions on Automatic Control. 2004, 49 (8): 1410–1413. doi:10.1109/tac.2004.832972. hdl:10945/29675.
- ^ F. Fahroo and I. M. Ross, "Advances in Pseudospectral Methods for Optimal Control," Proceedings of the AIAA Guidance, Navigation and Control Conference, AIAA 2008-7309. [1] （页面存档备份，存于互联网档案馆）
- ^ Wen, H.; Jin, D.; Hu, H. Infinite-Horizon Control for Retrieving a Tethered Subsatellite via an Elastic Tether. Journal of Guidance, Control and Dynamics. 2008, 31 (4): 889–906. doi:10.2514/1.33224.
- ^ 12.0 12.1 F. Fahroo and I. M. Ross, Pseudospectral Methods for Infinite Horizon Nonlinear Optimal Control Problems, AIAA Guidance, Navigation and Control Conference, August 15–18, 2005, San Francisco, CA.
- ^ 13.0 13.1 Fahroo, F.; Ross, I. M. Pseudospectral Methods for Infinite-Horizon Optimal Control Problems. Journal of Guidance, Control and Dynamics. 2008, 31 (4): 927–936. doi:10.2514/1.33117.
- ^ Ross, I. M.; Karpenko, M. A Review of Pseudospectral Optimal Control: From Theory to Flight. Annual Reviews in Control. 2012, 36 (2): 182–197 [2019-02-13]. doi:10.1016/j.arcontrol.2012.09.002. （原始内容存档于2015-09-24）.
- ^ N. S. Bedrossian, S. Bhatt, W. Kang, and I. M. Ross, Zero-Propellant Maneuver Guidance, IEEE Control Systems Magazine, October 2009 (Feature Article), pp 53–73.
- ^ F. Fahroo and I. M. Ross, Trajectory Optimization by Indirect Spectral Collocation Methods, Proceedings of the AIAA/AAS Astrodynamics Conference, August 2000, Denver, CO. AIAA Paper 2000–4028
- ^ Q. Gong, W. Kang, N. Bedrossian, F. Fahroo, P. Sekhavat and K. Bollino, Pseudospectral Optimal Control for Military and Industrial Applications, 46th IEEE Conference on Decision and Control, New Orleans, LA, pp. 4128–4142, Dec. 2007.
