Exact boundary synchronization for a kind of first order hyperbolic system

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-04-20 DOI:10.1051/cocv/2022031

Tatsien Li, Xing Lu

引用次数: 4

Abstract

In recent years there have been many in-depth researches on the boundary controllability and boundary synchronization for coupled systems of wave equations with various types of boundary conditions. In order to extend the study of synchronization from wave equations to a much larger range of hyperbolic systems, in this paper we will define and establish the exact boundary synchronization for the first order linear hyperbolic system based on previous work on its exact boundary controllability. The determination and estimate of exactly synchronizable states and some related problems are also discussed. This work can be applied to a great deal of diverse systems, and a new perspective to study the synchronization problem for the coupled system of wave equations can be also provided.

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一类一阶双曲型系统的精确边界同步

近年来，人们对具有各种边界条件的波动方程耦合系统的边界可控性和边界同步问题进行了深入的研究。为了将同步的研究从波动方程扩展到更大范围的双曲系统，本文在前人关于一阶线性双曲系统精确边界可控性的基础上，定义并建立了精确边界同步。讨论了精确同步状态的确定和估计及相关问题。这项工作可以应用于大量不同的系统，并为研究波动方程耦合系统的同步问题提供了一个新的视角。

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

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

自引率

7.10%

发文量

期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.