Numerical Study On Robust Optimal Control Of Stochastic Parabolic Equation

The optimization problem of partial differential equation constraint has wide applications in physics,biology and other fields.In recent years,scholars have made many achievements in the optimal control theory of certain partial differential equation.However,practical problems will are affected by random factors,and stochastic partial differential equations and optimal control problems have been concerned.This paper intends to study the numerical method for the robust optimal control problem of parabolic equations with random coefficient of the diffusion term.To study it directly is difficult.We first study the parametrized optimal control problem,where the solution is available as an initial guess value for solving the robust optimal control problem.Firstly,for the parametrized optimal control problem of parabolic,using the original Ensemble scheme discrete optimality system,we prove the uniqueness and stability of the Ensemble scheme,design the Ensemble algorithm for the parametrized optimal control problem of parabolic equation constraint,and present numerical experiments.The experimental results show that the given algorithm is effective.Secondly,based on the original Ensemble scheme,we present a new unconditionally stable Ensemble sampling method,which does not need to subgroup samples according to the stability conditions,and apply the method to the numerical simulation of the parametrized optimal control problem of parabolic equation constraint,the experimental results show that the new unconditionally stable Ensemble sampling method is efficient and feasible.Finally,in the course of numerical experiments we find that the solution is less robust in the Ensemble method than in the non-Ensemble scheme.For this purpose we propose the Ensemble Control variable method and apply this method to a robust optimal control problem.