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 infinite family of two dimensional LQRs each of which can be solved explicitly.

中文翻译：

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线性二次调节对梁方程的边界控制

我们提出并解决了线性二次调节器（LQR），用于束方程的边界控制。我们使用完成正方形的简单技术来获得明确的解决方案。通过解耦空间频率，我们能够将无限维LQR简化为二维LQR的无限族，每个线性LQR都可以显式求解。