Optimal boundary control of Saint-Venant equations with arbitrary friction and space-varying slope. (3rd June 2021)

• Record Type: Journal Article
• Authors: Wang, Yang-Yang; Sun, Bing
• Is Part Of: IMA journal of mathematical control and information. Volume 38:Number 3(2021)
• Page Start: 881
• Page End: 907
• Publication Date: 2021-06-03
• Subjects: Saint-Venant equations -- optimal control -- maximum principle -- necessary optimality condition; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnab016
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: This paper is concerned with the optimal boundary control for the one-dimensional Saint-Venant equations with arbitrary friction and space-varying slope. By the Dubovitskii and Milyutin functional analytical approach, the Pontryagin maximum principles of the optimal control systems equipped with two boundary control variables are investigated and the first-order necessary optimality conditions are presented in both the fixed and the free final horizon cases, respectively. Finally, a remark on numerical solution is made for illustrating how to apply the obtained results to the investigational optimal boundary control problem.