Abstract
Monte Carlo methods are applied to an open-loop calculation of affine nonlinear optimal control systems. Nonlinear optimal control systems are represented as an infinite sum or an integration of possible paths connecting initial and final points in their linear wave theories. Weight of each path is a trigonometric function of “action” integral along the path nondimensionalized by a characteristic control constant HR representing strength of fluctuations due to wave action. When this constant is set as a pure imaginary value, HR=iHR, trigonometric functions are transformed into exponential functions. We can then consider HR as “temperature” of Boltzmann distributions. The wave function is regarded as a statistical mean under the Boltzmann distribution. Optimal path satisfying conditions at two boundary points is given as a stationary phase of the wave function when the temperature HR is low. Simulation studies for a system with 1-input and 2-states are given.
