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

Guillaume Carlier; Rabah Tahraoui

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 ( $p < \infty$ ). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

Admissible relaxation in optimal control problems for infinite dimensional uncertain systems.

Ahmed, N.U., Xiang, X. (1992)

Journal of Applied Mathematics and Stochastic Analysis

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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: $inf_{(u, v) \in 𝒰_{a d}} \int_{0}^{1} f (t, u (θ_{v} (t)), u^{'} (t), v (t)) d t$ , (1) where $𝒰_{a d}$ is a set of admissible controls and $θ_{v}$ is the solution of the following equation: ${\frac{d θ (t)}{d t} = g (t, θ (t), v (t)), t \in [0, 1]$ ; $θ (0) = θ_{0}, θ (t) \in [0, 1] \forall t$ . (2). The results are nonlocal and new.

Optimal control of nonlinear second order evolution equations.

Ahmed, N.U., Kerbal, Sebti (1993)

Journal of Applied Mathematics and Stochastic Analysis

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Necessary conditions of optimality for infinite dimensional uncertain systems.

Ahmed, N.U., Xiang, X. (1995)

Mathematical Problems in Engineering

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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...

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

Admissible relaxation in optimal control problems for infinite dimensional uncertain systems.

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

Optimal control of nonlinear second order evolution equations.

Necessary conditions of optimality for infinite dimensional uncertain systems.

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

Relaxation of optimal control problems in $𝖫^{𝗉}$ -spaces