Special Session 19: Stochastic Partial Differential Equations

Approximation of Optimal Feedback Controls for Stochastic Reaction-Diffusion Equations

Alexander Vogler
TU Berlin
Co-Author(s):    Stannat, Wilhelm
We approximate optimal feedback controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the feedback function using finitely based approximations. Using structural assumptions on the finitely based approximations, rates for the approximation error of the cost can be obtained. Based on our approximation results we introduce a numerical algorithm that significantly reduces the computational complexity of finding controls with asymptotically optimal cost. Numerical experiments using artificial neural networks as well as radial basis function networks illustrate the performance of our algorithm. Our approach can also be applied to stochastic control problems for high dimensional stochastic differential equations and more general stochastic partial differential equations.