Adam Kowalewski, Anna Krakowiak (2008)
International Journal of Applied Mathematics and Computer Science
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In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.
Adam Kowalewski (2009)
International Journal of Applied Mathematics and Computer Science
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In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
S. Farag, M. Farag (2000)
Applicationes Mathematicae
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An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
Janković, Vladimir (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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Ira Neitzel, Fredi Tröltzsch (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated...
Madalina Petcu, Roger Temam (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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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.
Hongwei Lou (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.
M. Farag (1997)
Applicationes Mathematicae
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A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
Janković, Vladimir (1990)
Publications de l'Institut Mathématique. Nouvelle Série
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Vasilieva, Olga (2004)
International Journal of Mathematics and Mathematical Sciences
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Phuong Anh Nguyen, Jean-Pierre Raymond (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state....