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

The two contributions of this article 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.