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

• Autorzy: Klamka Jerzy , Avetisyan Ara S. , Khurshudyan Asatur Zh.

Identyfikatory

DOI

10.24425/acs.2020.132591

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

KdV equation; Boussinesq equation; Frasca’s method; short time expansion; traveling wave; heuristic method; distributed control; constrained controllability

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2020
• Tom: Vol. 30, No. 1
• Strony: 177--193
• Opis fizyczny: Bibliogr. 28 poz., rys., wykr., wzory

Twórcy

autor

Klamka Jerzy

• Institute of Control Engineering, Silesian University of Technology, Gliwice, Poland

autor

Avetisyan Ara S.

• Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia

autor

Khurshudyan Asatur Zh.

• Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia
• Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

Bibliografia

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Uwagi

EN

1. The work of the first author is supported by National Science Centre in Poland under grant: “Modelling, optimization and control for structural reduction of device noise”, no. UMO-2017/25/B/ST7/02236. The third author thankfully acknowledges the support of the State Administration of Foreign Experts Affairs of China.

PL

2. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).