Titre :

Mixed Deterministic and Random Optimal Control of Linear Stochastic Systems with Quadratic Costs

Auteur(s) :

Hu, Ying [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Tang, Shanjian [Auteur correspondant]

Titre de la revue :

Probability, Uncertainty and Quantitative Risk

Éditeur :

American Institute of Mathematical Sciences

Date de publication :

2019

ISSN :

2095-9672

Mot(s)-clé(s) en anglais :

Stochastic LQ
differential/algebraic Riccati equation
mixed deterministic and random control
singular LQ
infinite-horizon

Discipline(s) HAL :

Mathématiques [math]/Optimisation et contrôle [math.OC]

Résumé en anglais : [en]

In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers—one can choose only deterministic time functions, called the deterministic controller, ...
Lire la suite >In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers—one can choose only deterministic time functions, called the deterministic controller, while the other can choose adapted random processes, called the random controller. The optimal control is shown to exist under suitable assumptions. The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations (FB-SDEs) of mean-field type. We solve the FBSDEs via solutions of two (but decoupled) Riccati equations, and give the respective optimal feedback law for both determinis-tic and random controllers, using solutions of both Riccati equations. The optimal state satisfies a linear stochastic differential equation (SDE) of mean-field type. Both the singular and infinite time-horizonal cases are also addressed.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Jeux Champs Moyen
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL