Discontinuity, Nonlinearity, and Complexity
Partial Strong Stabilization of SemiLinear Systems and Robustness of Optimal Control
Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 369380  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
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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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