由KdV和Boussinesq方程描述的过程的精确和近似分布可控性:格林函数方法

IF 1.1 4区计算机科学 Q4 AUTOMATION & CONTROL SYSTEMS

Archives of Control Sciences Pub Date : 2023-07-20 DOI:10.24425/ACS.2020.132591

J. Klamka, A. Avetisyan, A. Khurshudyan

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引用次数: 1

摘要

本文利用格林函数方法研究了Korteweg-de Vries(三阶)和Boussinesq(四阶)半线性方程行波解的约束精确和近似可控性。控制是由一个移动的外部源执行的。用Frasca短时间展开式表示了这些方程的通解，导出了两种可控性的分布式控制约束系统。由于启发式方法提供显式解的可能性，使得可控性分析变得简单明了。数值分析证实了理论推导。

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Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach

In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis conﬁrms theoretical derivations.

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来源期刊

Archives of Control Sciences Mathematics-Modeling and Simulation

CiteScore

2.40

自引率

33.30%

发文量

审稿时长

14 weeks

期刊介绍： Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.