Optimal boundary control of Saint-Venant equations with arbitrary friction and space-varying slope. (3rd June 2021) - Wang, Yang-Yang; Sun, Bing
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.