POD-based feedback control of the burgers equation by solving the evolutionary HJB equation

A new approach for solving finite-time horizon feedback control problems for distributed parameter systems is proposed. It is based on model reduction by proper orthogonal decomposition combined with efficient numerical methods for solving the resulting low-order evolutionary Hamilton-Jacobi-Bellman (HJB) equation. The feasibility of the proposed methodology is demonstrated by means of optimal feedback control for the Burgers equation. The method for solving the HJB equation is first tested on several 1-D problems and then successfully applied to the control of the reduced order Burgers equation. The effect of noise is investigated, and parallelism is used for computational speedup.