Displaying similar documents to “Optimal control of semilinear parabolic equations with state-constraints of bottleneck type”

Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type

Maïtine Bergounioux, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear...

Relaxation of optimal control problems in 𝖫 𝗉 -spaces

Nadir Arada (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an L p -space ( p < ∞ ). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

Time-optimal boundary control of an infinite order parabolic system with time lags

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.

Control problems for convection-diffusion equations with control localized on manifolds

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....

Time-optimal boundary control of a parabolic system with time lags given in integral form

Adam Kowalewski, Anna Krakowiak (2006)

International Journal of Applied Mathematics and Computer Science

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In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.

Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints

Eduardo Casas (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that...

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel, Fredi Tröltzsch (2009)

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...