Tikhonov solutions of approximately controllable second-order semilinear control systems

被引：1
|
作者：
Singh, Soniya [1 ]
Dabas, Jaydev [1 ]
机构：
[1] Indian Inst Technol, Dept Appl Math & Sci Comp, Roorkee 247667, Uttarakhand, India
来源：
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2023年 / 72卷 / 04期
关键词：
Ill-posed problems; Cosine family; Approximate controllability; Tikhonov regularization; STOCHASTIC DIFFERENTIAL-EQUATIONS;
D O I：
10.1007/s12215-022-00802-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This manuscript considers a second-order semilinear control system in Hilbert space. By using Tikhonov regularization, we first construct the regularized control for the corresponding linear system and prove its approximate controllability. We then establish approximate controllability results using Gronwall's Lemma for the semilinear system. In addition, the error estimates and convergence rates involved in the regularization procedure are also obtained. Further, we give an example to demonstrate the results.
引用
收藏
页码：2375 / 2387
页数：13
相关论文
共 50 条
  • [1] Tikhonov solutions of approximately controllable second-order semilinear control systems
    Soniya Singh
    Jaydev Dabas
    Rendiconti del Circolo Matematico di Palermo Series 2, 2023, 72 : 2375 - 2387
  • [2] The Controllability for Second-Order Semilinear Impulsive Systems
    Wen, Qian
    Feckan, Michal
    Wang, JinRong
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2023, 22 (01)
  • [3] Controllability of second-order nonlocal retarded semilinear systems with delay in control
    Haq, Abdul
    Sukavanam, N.
    APPLICABLE ANALYSIS, 2020, 99 (16) : 2741 - 2754
  • [4] Computation of Control for Linear Approximately Controllable System Using Tikhonov Regularization
    Nair, M. Thamban
    Sukavanam, N.
    Katta, Ravinder
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (03) : 308 - 321
  • [5] Computation of control for nonlinear approximately controllable system using Tikhonov regularization
    Katta, Ravinder
    Sukavanam, N.
    COGENT MATHEMATICS, 2016, 3
  • [6] Approximate Controllability of Second-Order Semilinear Control System
    Shukla, Anurag
    Sukavanam, N.
    Pandey, D. N.
    Arora, Urvashi
    CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2016, 35 (09) : 3339 - 3354
  • [7] Approximate Controllability of Second-Order Semilinear Control System
    Anurag Shukla
    N. Sukavanam
    D. N. Pandey
    Urvashi Arora
    Circuits, Systems, and Signal Processing, 2016, 35 : 3339 - 3354
  • [8] Results on exact controllability of second-order semilinear control system in Hilbert spaces
    Arora, Urvashi
    Vijayakumar, V.
    Shukla, Anurag
    Nisar, Kottakkaran Sooppy
    Rezapour, Shahram
    Jamshed, Wasim
    ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)
  • [9] Approximate Controllability of Second-order Semilinear Evolution Systems with Finite Delay
    Xiao-feng Su
    Xian-long Fu
    Acta Mathematicae Applicatae Sinica, English Series, 2021, 37 : 573 - 589
  • [10] Approximate Controllability of Second-order Semilinear Evolution Systems with Finite Delay
    Su, Xiao-feng
    Fu, Xian-long
    ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2021, 37 (03): : 573 - 589
12345