Optimal distributed control problem for the modified Swift-Hohenberg equations

Abstract

This article concerns the optimal distributed control for the modified Swift-Hohenberg equation. Using the Dubovitskii and Milyutin functional analytical approach, we prove the Pontryagin maximum principle of the controlled modified Swift-Hohenberg equation. A necessary optimality condition is established for the problem in fixed final time horizon case. Also we indicate how to utilize the obtained results.

Keywords

• Maximum principle
• optimal distributed control
• necessary optimality condition
• Swift-Hohenberg equation