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

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 HR to a pure imaginary value, HR=iHR is applied to these path integrals. Wave functions are then calculated as statistical mean values under the Boltzmann distributions with temperatures proportional to HR, 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.