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~β0 to HamiltonβJacobi 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 noβsingularity condition. Although we restrict ourselves to scalar systems, generalization to systems with higher dimensionality is straightforward. Β© 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 161(4): 29β37, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20521