Displaying similar documents to “On some optimal control problems governed by a state equation with memory”

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.

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.

Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation

Anar Huseyin, Nesir Huseyin (2014)

Applications of Mathematics

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In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius μ in L p ( p > 1 ) . It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to μ for each fixed p , and is continuous with respect to p for each fixed...