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Ross' lemma, named after I. Michael Ross,〔 B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Vol. 330 of Grundlehren der Mathematischen Wissenschaften (Principles of Mathematical Sciences ) Series, Springer, Berlin, 2005. 〕〔 W. Kang, "Rate of Convergence for the Legendre Pseudospectral Optimal Control of Feedback Linearizable Systems", Journal of Control Theory and Application, Vol.8, No.4, 2010. pp. 391-405. 〕〔 Jr-S Li, J. Ruths, T.-Y. Yu, H. Arthanari and G. Wagner, "Optimal Pulse Design in Quantum Control: A Unified Computational Method", Proceedings of the National Academy of Sciences, Vol.108, No.5, Feb 2011, pp.1879-1884. 〕 is a result in computational optimal control. Based on generating Carathéodory- solutions for feedback control, Ross' -lemma states that there is fundamental time constant within which a control solution must be computed for controllability and stability. This time constant, known as Ross' time constant,〔 N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorithms Boost Satellite Performance on the Cheap" IEEE Spectrum, November 2012. 〕〔 R. E. Stevens and W. Wiesel, "Large Time Scale Optimal Control of an Electrodynamic Tether Satellite", Journal of Guidance, Control and Dynamics, Vol. 32, No. 6, pp. 1716–1727, 2008. 〕 is proportional to the inverse of the Lipschitz constant of the vector field that governs the dynamics of a nonlinear control system.〔I. M. Ross, P. Sekhavat, A. Fleming and Q. Gong, "Optimal Feedback Control: Foundations, Examples, and Experimental Results for a New Approach", ''Journal of Guidance, Control, and Dynamics'', vol. 31 no. 2, pp. 307–321, 2008. 〕〔I. M. Ross, Q. Gong, F. Fahroo, and W. Kang, "Practical Stabilization Through Real-Time Optimal Control", 2006 American Control Conference, Inst. of Electrical and Electronics Engineers, Piscataway, NJ, 14–16 June 2006.〕 ==Theoretical implications== The proportionality factor in the definition of Ross' time constant is dependent upon the magnitude of the disturbance on the plant and the specifications for feedback control. When there are no disturbances, Ross' -lemma shows that the open-loop optimal solution is the same as the closed-loop one. In the presence of disturbances, the proportionality factor can be written in terms of the Lambert W-function. 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「Ross' π lemma」の詳細全文を読む スポンサード リンク
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