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Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition. (English) Zbl 0949.93039
Summary: 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.
MSC:
93C20Control systems governed by PDE
93B40Computational methods in systems theory