Some results on convergence linked to a perturbed boundary optimal control system.
A. Bounabat, T. Benkiran, M. Akkouchi (1994)
Extracta Mathematicae
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A. Bounabat, T. Benkiran, M. Akkouchi (1994)
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Yuncheng You (1996)
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Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear...
V. Janković (1981)
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J. L. Gámez, J. A. Montero (1997)
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Noriaki Yamazaki (2009)
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In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results. ...
Boscain, U., Piccoli, B. (1998)
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Pedro Humberto Rivera Rodriguez (1984)
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Madalina Petcu, Roger Temam (2010)
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In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.