Boundary Control of the Beam Equation by Linear Quadratic Regulation

TL;DR

This paper develops an explicit boundary control strategy for the beam equation using a Linear Quadratic Regulator, simplifying the infinite-dimensional problem into manageable two-dimensional subproblems.

Contribution

It introduces a novel explicit solution for boundary control of the beam equation via LQR by decoupling spatial frequencies, reducing complexity.

Findings

Explicit boundary control solution derived

Decoupling spatial frequencies simplifies the infinite-dimensional problem

LQR applied effectively to beam equation boundary control

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.