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

被引：3
|
作者：
Klamka, Jerzy [1 ]
Avetisyan, Ara S. [2 ]
Khurshudyan, Asatur Zh [2 ,3 ]
机构：
[1] Silesian Tech Univ, Inst Control Engn, Gliwice, Poland
[2] Natl Acad Sci Armenia, Inst Mech, Dept Dynam Deformable Syst & Coupled Fields, Yerevan, Armenia
[3] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai, Peoples R China
来源：
ARCHIVES OF CONTROL SCIENCES | 2020年 / 30卷 / 01期
关键词：
KdV equation; Boussinesq equation; Frasca's method; short time expansion; traveling wave; heuristic method; distributed control; constrained controllability; CONSTRAINED CONTROLLABILITY;
D O I：
10.24425/acs.2020.132591
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
引用
收藏
页码：177 / 193
页数：17
相关论文
共 26 条
  • [1] Green's function approach in approximate controllability for nonlinear physical processes
    Avetisyan, Ara S.
    Khurshudyan, Asatur Zh.
    MODERN PHYSICS LETTERS A, 2017, 32 (21)
  • [2] Exact and approximate controllability of nonlinear dynamic systems in infinite time: The Green's function approach
    Avetisyan, Ara S.
    Khurshudyan, Asatur Zh.
    ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2018, 98 (11): : 1992 - 2009
  • [3] Resolving controls for exact and approximate controllability of viscous Burgers' equation: The Green's function approach
    Khurshudyan, Asatur Zh.
    INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2018, 29 (06):
  • [4] Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green's function approach
    Khurshudyan, Asatur Zh
    ARCHIVES OF CONTROL SCIENCES, 2018, 28 (03): : 335 - 347
  • [5] Green's functions for higher order nonlinear equations Case studies for KdV and Boussinesq equations
    Frasca, Marco
    Khurshudyan, Asatur Zh
    INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2018, 29 (10):
  • [6] Resolving Controls for the Boundary Approximate Controllability of Sandwich Beams with Uncertainties the Green’s Function Approach
    As. Zh. Khurshudyan
    Sh. Kh. Arakelyan
    Mechanics of Composite Materials, 2019, 55 : 85 - 94
  • [7] RESOLVING CONTROLS FOR THE BOUNDARY APPROXIMATE CONTROLLABILITY OF SANDWICH BEAMS WITH UNCERTAINTIES THE GREEN'S FUNCTION APPROACH
    Khurshudyan, As. Zh.
    Arakelyan, Sh. Kh.
    MECHANICS OF COMPOSITE MATERIALS, 2019, 55 (01) : 85 - 94
  • [8] Distributed controllability of one-dimensional heat equation in unbounded domains: The Green's function approach
    Khurshudyan, Asatur Zh
    ARCHIVES OF CONTROL SCIENCES, 2019, 29 (01): : 57 - 71
  • [9] Exact Green's function approach to RKKY interactions
    Rusin, Tomasz M.
    Zawadzki, Wlodek
    PHYSICAL REVIEW B, 2020, 101 (20)
  • [10] Exact dynamical reorientation in nematic liquid crystals: Green's function approach
    Yednak, C. A. R.
    Igarashi, R. N.
    Lenzi, E. K.
    Evangelista, L. R.
    PHYSICS LETTERS A, 2006, 358 (01) : 31 - 36
123