Robust boundary control of systems of conservation laws
Robust boundary control of systems of conservation laws
复制标题
DOI：
10.1007/s00498-008-0028-x
复制
发表时间：
2008-05
期刊：
影响因子：
--
通讯作者：
C. Prieur;J. Winkin;G. Bastin
中科院分区：
文献类型：
--
作者：
C. Prieur;J. Winkin;G. Bastin
研究了由非齐次项扰动的守恒律系统的稳定性问题。假设这些非齐次项有一个小的c1范数。利用黎曼坐标法建立了边界条件下的充分稳定性判据。对于受外部扰动的守恒律系统，该判据可以通过边界控制解释为鲁棒稳定条件。然后将这一稳定性结果应用于明渠中水位和流量的调节问题。通道中的水流由圣维南方程描述，该方程被小的非齐次项扰动，这些项考虑了摩擦效应以及外部供水或提取。
The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a smallC1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization condition by means of a boundary control, for systems of conservation laws subject to external disturbances. This stability result is then applied to the problem of the regulation of the water level and the flow rate in an open channel. The flow in the channel is described by the Saint-Venant equations perturbed by small non-homogeneous terms that account for the friction effects as well as external water supplies or withdrawals.