Title :

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

Author(s) :

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

Journal title :

Probability, Uncertainty and Quantitative Risk

Publisher :

American Institute of Mathematical Sciences

Publication date :

2019

ISSN :

2095-9672

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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, ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Jeux Champs Moyen

Collections :

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

Source :

Harvested from HAL