Abstract

In this paper, we consider the problem about the simultaneous realization of exact boundary controllability of final state and nodal profile for general 1-D first order quasilinear hyperbolic systems. We show that by means of boundary controls, the system (hyperbolic equations together with boundary conditions) can drive any given initial data at \(t=0\) to any given final data at \(t=T\) , and the solution to the system fits exactly any given nodal profile on a boundary node or an internal node for certain subinterval \([T_1,T_2]\) of [0, T]. Moreover, we give an application of the main results to the system of traffic flow.

中文翻译：

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拟线性双曲系统最终状态和节点轮廓的同时精确边界可控性

摘要

在本文中，我们考虑同时实现一般一维一阶拟线性双曲系统最终状态和节点轮廓的精确边界可控性的问题。我们证明，通过边界控制，系统（双曲方程与边界条件一起）可以将\(t=0\)处的任何给定初始数据驱动到\(t=T\)处的任何给定最终数据，并且解对于[0,  T ] 的某些子区间\([T_1,T_2]\)，系统完全拟合边界节点或内部节点上的任何给定节点轮廓。此外，我们还将主要结果应用到交通流系统中。