Numerical Calculation of Feedback Law in Quantum Mechanical Theory of Optimal Control
A numerical method of calculating feedback law in quantum mechanical theory of nonlinear optimal control is proposed. We clarify how to derive the feedback formula using a transformation of a characteristic control constant HR into a pure imaginary number iH̃R, which has so far been applied only heuristically. After setting an absolute value of a wave function at terminal time as a function without no singularity in HR, a phase part of the wave function is expanded as a Taylor series in HR. According to the expansion, an explicit formula of the feedback law in terms of H̃R is given. This formula fits numerical methods, because the wave function utilized in the formula meets an appropriate spatial boundary condition imposed on generalized Schrödinger equation.Validity of the feedback formula is shown by a numerical simulation study.