Control of Fractional Diffusion Problems via Dynamic Programming Equations

We explore the approximation of feedback control integro-differential equations containing a fractional Laplacian term. To obtain for state variable this nonlocal equation, we use Hamilton–Jacobi–Bellman equation. It is well known that approach suffers from curse dimensionality, and to mitigate problem couple semi-Lagrangian schemes discretization dynamic programming principle with Shepard approximation. This coupling enables high-dimensional problems. Numerical convergence toward solution continuous provided together linear nonlinear examples. The robustness method respect disturbances system illustrated by comparisons an open-loop approach.