一类随机最优控制问题的拟蒙特卡洛方法

A QuasiMonte Carlo Method for a Class of Stochastic Optimal Control Problems

本文使用梯度投影优化方法求解一类随机最优控制问题.蒙特卡洛方法是处理随机最优控制问题的一种常用方法,但收敛速度慢.我们选取收敛速度较快的拟蒙特卡洛方法.为使随机抽样维数和时间离散点独立,我们对Brown运动进行Karhunen-Loève截断,用拟蒙特卡洛方法中Sobol点序列抽样,得出数值近似的误差,并通过数值实验验证方法的有效性.

In this paper,a gradient projection optimization method is applied to solve a class of stochastic optimal control problems.The Monte Carlo method is a common method to deal with stochastic optimal control problems,but it has a notoriously slow convergence rate.We choose the Quasi­-Monte Carlo method with faster convergence.In order to make the random sampling dimensions and time discrete points independent,we use the Karhunen­Loève truncation for the Brown motion.Sobol sequences of the Quasi­-Monte Carlo method are used for sampling.The error of numerical approximation is presented,and the effectiveness of the method is verified by numerical experiments.