Nonlinear Optimal Control by Monte-Carlo Methods Applied to Path Integrals

Abstract

Nonlinear optimal control using Monte-Carlo calculation of path integrals is proposed. Wave functions appearing in a quantum mechanical theory of nonlinear optimal control are represented as superposition of various paths connecting initial and final points. A transformation of a characteristic designer's constant H_R to a pure imaginary value, H_R=iH_R is applied to these path integrals. Wave functions are then calculated as statistical mean values under the Boltzmann distributions with temperatures proportional to H_R, the transformed values of the designer, s constant. Monte-Carlo methods enforced by Metropolis algorithm are then applied to evaluate wave functions and optimal control calculations. Validities of proposed scheme will be shown in simple systems with 1-input and 1-state variables.