Simultaneous Exact Boundary Controllability of Final State and Nodal Profile for Quasilinear Hyperbolic Systems

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-02-26 DOI:10.1007/s00245-024-10111-y

Libin Wang, Mingming Zhang

引用次数: 0

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.

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准线性双曲系统最终状态和节点轮廓的同步精确边界可控性

摘要本文考虑了一般一维一阶准线性双曲系统的最终状态和节点轮廓的精确边界可控性的同时实现问题。我们证明，通过边界控制，系统（双曲方程和边界条件）可以驱动任意给定的初始数据在 \(t=0\) 到任意给定的最终数据在 \(t=T\) ，并且系统的解完全符合[0, T]的某个子区间 \([T_1,T_2]\) 的边界节点或内部节点上的任意给定的节点轮廓。此外，我们还给出了主要结果在交通流系统中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.