标量守恒律的反馈控制及其在高速公路密度控制中的应用：通过可变速度限制
Feedback Control of Scalar Conservation Laws with Application to Density Control in Freeways by Means of Variable Speed Limits
AI总结：
本文研究了通过可变速度限制控制交通动态中标量守恒律的稳定性问题，提出两种控制策略并给出反馈律公式，实现全局渐近稳定和区域指数稳定，且闭环系统解为经典解，无激波。
摘要：
本文提供了关于通过可变速度限制控制交通动态中标量守恒律空间均匀平衡剖面稳定性的结果。研究了两种不同的控制问题：入口处有自由速度限制和无入口速度限制的问题。分别给出了相应的反馈律公式，保证了所期望的平衡剖面的稳定。对于第一个问题，实现了全局渐近稳定；而对于第二个问题，实现了区域指数稳定。此外，对应的闭环系统解被保证为经典解，即不存在激波。所获得的结果通过数值例子进行了说明。
英文摘要：
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are studied: the problem with free speed limits at the inlet and the problem with no speed limits at the inlet. Explicit formulas are provided for respective feedback laws that guarantee stabilization of the desired equilibrium profile. For the first problem, global asymptotic stabilization is achieved; while for the second problem, regional exponential stabilization is achieved. Moreover, the solutions for the corresponding closed-loop systems are guaranteed to be classical solutions, i.e., there are no shocks. The obtained results are illustrated by means of a numerical example.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
