Existence and optimality conditions for relaxed mean-field stochastic control problems

Khaled Bahlali; Meriem Mezerdi; Brahim Mezerdi

doi:10.1016/j.sysconle.2016.12.009

Existence and optimality conditions for relaxed mean-field stochastic control problems

Khaled Bahlali
, Meriem Mezerdi
, Brahim Mezerdi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjoint processes extending the known results to the case of relaxed controls.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Systems and Control Letters
Volume	102
DOIs	https://doi.org/10.1016/j.sysconle.2016.12.009
State	Published - 1 Apr 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

Adjoint process
Martingale measure
Mean-field stochastic differential equation
Relaxed control
Stochastic maximum principle
Variational principle

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/j.sysconle.2016.12.009

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title = "Existence and optimality conditions for relaxed mean-field stochastic control problems",

abstract = "We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjoint processes extending the known results to the case of relaxed controls.",

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T1 - Existence and optimality conditions for relaxed mean-field stochastic control problems

AU - Bahlali, Khaled

AU - Mezerdi, Meriem

AU - Mezerdi, Brahim

PY - 2017/4/1

Y1 - 2017/4/1

N2 - We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjoint processes extending the known results to the case of relaxed controls.

AB - We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is driven by an orthogonal martingale measure, whose covariance measure is the relaxed control. This is a natural extension of the original strict control problem, for which we prove the existence of an optimal control. Then, we derive optimality necessary conditions for this problem, in terms of two adjoint processes extending the known results to the case of relaxed controls.

KW - Adjoint process

KW - Martingale measure

KW - Mean-field stochastic differential equation

KW - Relaxed control

KW - Stochastic maximum principle

KW - Variational principle

UR - https://www.scopus.com/pages/publications/85010461780

U2 - 10.1016/j.sysconle.2016.12.009

DO - 10.1016/j.sysconle.2016.12.009

M3 - Article

AN - SCOPUS:85010461780

SN - 0167-6911

VL - 102

SP - 1

EP - 8

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

Existence and optimality conditions for relaxed mean-field stochastic control problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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