ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Partial Strong Stabilization of Semi-Linear Systems and Robustness of Optimal Control

Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 369--380 | DOI:10.5890/DNC.2021.09.002

A. El Alami$^1$ , M. Chqondi$^2$, Y. Akdim$^2$

$^1$ Research Center STIS, Team M2CS, Department of Applied Mathematics and Informatics, ENSAM, Mohammed V University in Rabat, Madinat Al Irfane, Rabat, Morocco

$^2$ Laboratory of Mathematical Analysis & Application, Department of Mathematics and Informatics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, FES, Morocco

Abstract

This work addresses the idea of optimal stabilization, namely robustness of optimal stabilization with nonlinearity Lipschitz of distributed semilinear systems using bounded control. This problem is treated under the condition of the unbounded operator, we show that the system is stable once the exact observability assumption is executed together with a Lipschitz property of the nonlinear operator. The concept of bounded control is also investigated in realistic domain. The stabilizing feedback is characterized by the minimization of the problem of cost. We also give different applications to parabolic and hyperbolic equations.

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