论文标题
稳定双曲线平衡定律的多维系统
Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws
论文作者
论文摘要
我们对Hamilton-Jacobi类型方程在$ \ Mathbb {r}^n $中描述的系统的反馈稳定感兴趣。重新制定导致$ N $双曲线部分微分方程的多维系统的稳定问题。使用新颖的Lyapunov功能考虑到多维几何形状，我们使用合适的反馈控制显示了$ l^2 $的稳定化。我们进一步介绍了基于形成过程的部分示例。
We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $L^2$ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.
