Boundary control of Burgers' equation—a numerical approach

AbstractWe describe a methodology for solving boundary control problems for the viscous Burgers' equation. The aim is to identify boundary forcing in order to ensure the “best” fit between data and model results, by minimizing a functional which measures model and data discrepancies. A continuous variational formulation involving the adjoint technique is used, and its counterpart discretized version is obtained with a matrix approach as a guideline. A particular discretization of the nonlinear term of the equation is performed in order to insure, for the gradient of the functional to be minimized, a discretized expression which can be directly deduced from its continuous counterpart. Numerical experiments validate the proposed optimization algorithm