HJB-RBF Based Approach for the Control of PDEs

Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time projected state-space grid. The use structured grid makes this approach not feasible high-dimensional problems due to curse dimensionality. Here, we present new infinite horizon optimal control where value function is computed using Radial Basis Functions (RBF) by Shepard's moving least squares approximation method scattered grids. We propose generate mesh driven dynamics and selection shape parameter in RBF an optimization routine. This will help localize problem approximate high dimension. Error estimates also provided. Numerical tests dimensional show effectiveness proposed method.