RBF-based 2D optimal spatial control of the 3D reaction-convection-diffusion equation

Solving optimal control problems for spatially-distributed systems with multiple spatial dimensions can be computationally expensive. A numerical algorithm is proposed that combines a radial basis function expansion for the target trajectory with moment analysis. The approach is applicable to optimal control problems for linear spatially-distributed systems, for which the solution is expressed as a convolution of the system´s kernel and its inputs. A novel feature is the insensitivity of its computational cost to the sharpness of spatial variations in the state or optimal control fields. This approach is applied to the optimal control of the three-dimensional reaction-convection-diffusion equation in which the control input and target are defined over two-dimensional spatial fields.