Optimal Boundary Control of a Nonlinear Reaction Diffusion Equation via Completing the Square and Al'brekht's Method

TL;DR

This paper develops a constructive method for optimal boundary control of nonlinear reaction diffusion systems, extending classical techniques to infinite-dimensional settings for improved stabilization strategies.

Contribution

It introduces a simple completing the square approach for boundary LQR problems and extends Al'brekht's method to nonlinear reaction diffusion systems.

Findings

Successfully solves boundary LQR via completing the square.

Extends Al'brekht's method to nonlinear boundary control.

Provides a constructive framework for stabilization of reaction diffusion equations.

Abstract

The two contributions of this paper are as follows. The first is the solution of an infinite dimensional, boundary controlled Linear Quadratic Regulator by the simple and constructive method of completing the square. The second contribution is the extension of Al'brekht's method to the optimal stabilization of a boundary controlled, nonlinear Reaction Diffusion system.