Boundary Control of the Beam Equation by Linear Quadratic Regulation

Abstract: We present and solve a Linear Quadratic Regulator (LQR) for the boundary control of the beam equation. We use the simple technique of completing the square to get an explicit solution. By decoupling the spatial frequencies we are able to reduce an infinite dimensional LQR to an infinte family of two two dimensional LQRs each of which can be solved explicitly.