Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition

Proper orthogonal decomposition (POD) is a method to derive reduced-order models for dynamical systems. In this paper, POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation. The relative simplicity of the equation allows comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system. For closed-loop control, suboptimal state feedback strategies are presented.