Discontinuity, Nonlinearity, and Complexity
Strong Stabilization of Inhomogeneous Semilinear Systems
Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 373--385 | DOI:10.5890/DNC.2024.06.014
A. El Alami$^{1}$, M. Chqondi$^{2}$
$^{1}$ Research Center STIS, Team M2CS, Department of Applied Mathematics and Informatics, ENSAM,
Mohammed V University in Rabat, Madinat Al Irfane, Rabat, Morocco
$^{2}$ Laboratory LAMA, Department of Mathematics and Informatics, Sidi Mohamed Ben Abdellah University,
Faculty of Sciences Dhar El Mahraz, FES, Morocco
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Abstract
In this paper we study feedback stabilization of inhomogeneous semi-linear control system on a Hilbert state space. The paper gives a feedback control that ensure the strong in term of approximate observability like assumptions. Applications to heat equations are provided.
References
-
[1]  |
Shah, K., Jarad, F., and Abdeljawad, T. (2020), Stable numerical results to a class of time-space fractional partial differential equations via spectral method, Journal of Advanced Research, 25, 39-48.
|
-
[2]  |
Kukreja, V.K. (2022), Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method, Journal of Ocean Engineering and Science, 7(2), 99-111.
|
-
[3]  |
Ahmad, H., Seadawy, A.R., and Khan, T.A. (2020), Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm, Mathematics and Computers in Simulation, 177, 13-23.
|
-
[4]  |
Ahmad, H., Seadawy, A.R., Khan, T.A., and Thounthong, P. (2020), Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations, Journal of Taibah University for Science,14(1), 346-358.
|
-
[5]  |
Harraki, I.E., Alami, A.E., Boutoulout, A., and Serhani, M. (2017), Regional stabilization of semi-linear parabolic systems, Journal of Mathematical Control and Information, 34(3), 961-971
|
-
[6]  |
Gugat, M. and Tr\"oltzsch, F. (2015), Boundary feedback stabilization of the Schl\"ogl system,
Automatica, 51, 192-199.
|
-
[7]  |
Ouzahra, M. (2009), Stabilisation of infinite-dimensional bilinear systems using a quadratic feedback control, International Journal of Control, 82(9), 1657-1664.
|
-
[8]  |
El-Farra, N.H. and Christofides, P.D. (2004), Coordinating feedback and switching for control of spatially distributed processes, Computers and Chemical Engineering, 28(1-2), 111-128.
|
-
[9]  |
Gugat, M. and Sigalotti, M. (2010), Stars of vibrating strings: switching boundary feedback stabilization, Networks and Heterogeneous Media, 5(2), 299-314.
|
-
[10]  |
Gugat, M. (2008), Optimal switching boundary control of a string to rest in finite time, Journal of Applied Mathematics and Mechanics/Zeitschrift f\"ur Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, 88(4), 283-305
|
-
[11]  |
Gugat, M. and Tucsnak, M. (2011), An example for the switching delay feedback stabilization of an infinite dimensional system: The boundary stabilization of a string, Systems and Control Letters, 60(4), 226-233.
|
-
[12]  |
Ouzahra, M. (2010), Exponential and weak stabilization of constrained bilinear systems, SIAM Journal on Control and Optimization, 48(6), 3962-3974.
|
-
[13]  |
Ball, J.M. and Slemrod, M. (1979), Feedback stabilization of distributed semilinear control systems, Applied Mathematics and Optimization, 5(1), 169-179.
|
-
[14]  |
Hamidi, Z. and Ouzahra, M. (2018), Partial stabilisation of non-homogeneous bilinear systems, International Journal of Control, 91(6), 1251-1258.
|
-
[15]  |
Martin, Jr. and Robert, H. and Pazy, A. (1985), Semigroups of linear operators and applications to partial differential equations, Bulletin Bulletin (New Series) of the American Mathematical Society, 12(2), 302-305.
|
-
[16]  |
El Alami, A., Chqondi, M., and Akdim, Y. (2021), Partial strong stabilization of semi-linear systems and robustness of optimal control, Discontinuity, Nonlinearity, and Complexity, 10(03), 369-380.
|
-
[17]  |
Akkouchi, M. and Bounabat, A. (2003), Weak stabilizability of a nonautonomous and non-linear system,
Mathematica Pannonica, 14(1), 55-61.
|
-
[18]  |
Ball, J.M. (1977), Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proceedings of the American Mathematical Society, 63(2), 370-373.
|
-
[19]  |
Zine, R. and El Alami, A. (2020), Strong and weak stabilization of semi-linear parabolic systems, Journal of Mathematical Control and Information, 37(1), 50-63.
|