Strong Stabilization of Inhomogeneous Semilinear Systems
DOI:
https://doi.org/10.5890/DNC.2024.06.014Abstract
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 Tröltzsch, F. (2015), Boundary feedback stabilization of the Schlögl 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 für 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.
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