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

• 成果类型: Article
• 署名作者: Krener, Arthur J.
• 署名单位: United States Department of Defense; United States Navy; Naval Postgraduate School
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3121233
• 发表日期: 2022
• 页码: 6698-6709
• 关键词: Boundary conditions; Heating systems; COSTS; mathematical models; Integral equations; GOVERNMENT; Boundary control of an LQR; computational methods; distributed parameter system; optimal control

摘要

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.