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Quantum fluctuation in affine optimal control systems
Author(s) -
Itami Teturo
Publication year - 2007
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.20521
Subject(s) - singularity , planck constant , quantum , mathematics , constant (computer programming) , scalar (mathematics) , wave function , physics , quantum mechanics , mathematical physics , affine transformation , limit (mathematics) , amplitude , mathematical analysis , pure mathematics , computer science , geometry , programming language
Abstract Quantum mechanical wave functions are shown to approximate optimal feedback laws of affine control systems, when we set the absolute values of the terminal wave functions positive and with no singular dependence on a control constant H R , which is similar in position to the action constant $\hbar$ introduced by Planck to explain quantum phenomena. Calculation of the wave functions makes use of the path integral representation that we approximate at stationary phase. The phases of the wave functions approximate in H R →0 to Hamilton–Jacobi value functions, because quantum mechanical fluctuation vanishes in the limit. It is simple to take the terminal absolute value function that meets the condition of having no singularity at H R =0. The terminal absolute value function without any dependence on the constant H R apparently satisfies the no‐singularity condition. Although we restrict ourselves to scalar systems, generalization to systems with higher dimensionality is straightforward. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 161(4): 29–37, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20521