本项目拟研究具回路的无摩擦水平开河道网络和有摩擦倾斜开河道网络上一维Saint-Venant方程模型这类在物理、力学、工程科学等学科中出现的重要的非线性双曲守恒律系统模型的能控性。Saint-Venant方程组作为水利工程中处理水流动力学模型的标准工具，其能控性的研究一直是一个十分活跃的方向。网络上非线性双曲守恒律系统的控制问题，由于其应用的广泛性，是近代应用数学一个热点的前沿研究方向，而具回路的网络上的非线性双曲守恒律系统，由于复杂性和多样性，能控性的研究还基本处于空白阶段。对具回路的网络上Saint-Venant 方程组能控性的研究，不仅能引出新的理论和方法，而且可以推动非线性双曲守恒律系统控制理论的发展。

The project will study the problems of controllability for two nonlinear hyperbolic systems of conservation laws: 1-D Saint-Venant system for horizontal frictionless in a network of open canals with loops, and 1-D Saint-Venant system for sloped canals with friction in a network of open canals with loops. As a standard tool for solving engineering problems regarding the dynamics of canals and rivers, the controllability of Saint-Venant equations always attract researchers' attention. The controllability for nonlinear hyperbolic systems of conservation laws is a forward direction in modern mathematics for its widespread applications. While for nonlinear hyperbolic systems of conservation laws in a network of open canals with loops, there is no much result about its controllability. Therefore, an intensive study on these problems not only needs creativities on both theories and applications, but also brings important impacts on the research on nonlinear hyperbolic systems of conservation laws.