28-31 August 2018
Angers - France
Europe/Paris timezone

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

29 Aug 2018, 14:40
40m
Angers - France

Angers - France

Speaker

Prof. Shanjian Tang (Fudan University, School of Mathematical Science)

Description

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 (FBSDEs) 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 deterministic 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.

This is a joint work with Ying HU, Universite de Rennes 1.

Primary author

Prof. Shanjian Tang (Fudan University, School of Mathematical Science)

Co-author

Prof. Ying Hu (Université Rennes 1)

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