Displaying similar documents to “Relaxation of optimal control problems in 𝖫 𝗉 -spaces”

How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) ∈ 𝒰 a d ∫ 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t ∈ [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) ∈ [ 0 , 1 ] ∀ t . (2). The results are nonlocal and new.

On some optimal control problems governed by a state equation with memory

Guillaume Carlier, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to study problems of the form: i n f ( u ∈ V ) J ( u ) with J ( u ) : = ∫ 0 1 L ( s , y u ( s ) , u ( s ) ) d s + g ( y u ( 1 ) ) where is a set of admissible controls and is the solution of the Cauchy problem: x ˙ ( t ) = 〈 f ( . , x ( . ) ) , ν t 〉 + u ( t ) , t ∈ ( 0 , 1 ) , x ( 0 ) = x 0 and each ν t is a nonnegative measure with support in . After studying the Cauchy problem, we establish existence of minimizers, optimality conditions (in particular in the form of a nonlocal version of the Pontryagin principle) and prove some regularity results. We also consider the more general case where the control...

Optimal control of a rotating body beam

Weijiu Liu (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose...

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....

Regional control problem for distributed bilinear systems: Approach and simulations

Karima Ztot, El Hassan Zerrik, Hamid Bourray (2011)

International Journal of Applied Mathematics and Computer Science

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This paper investigates the regional control problem for infinite dimensional bilinear systems. We develop an approach that characterizes the optimal control and leads to a numerical algorithm. The obtained results are successfully illustrated by simulations.