{"title":"Simultaneous Exact Boundary Controllability of Final State and Nodal Profile for Quasilinear Hyperbolic Systems","authors":"Libin Wang, Mingming Zhang","doi":"10.1007/s00245-024-10111-y","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(t=0\\)</span> to any given final data at <span>\\(t=T\\)</span>, and the solution to the system fits exactly any given nodal profile on a boundary node or an internal node for certain subinterval <span>\\([T_1,T_2]\\)</span> of [0, <i>T</i>]. Moreover, we give an application of the main results to the system of traffic flow.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 2","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-024-10111-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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