Probability & Statistics Seminar

Optimal feedback for stochastic linear quadratic control in infinite dimensions, progress and open problems

  • Speaker: Xu Zhang (Sichuan University)

  • Time: Apr 13, 2022, 16:00-17:00

  • Location: Tencent Meeting ID 813 145 874

Abstract

In this talk, I will present my work (jointly with Qi Lü) on characterization of optimal feedback for stochastic linear quadratic control in infinite dimensions by means of Riccati type equations. More precisely, under some assumptions which can be verified for interesting concrete models, we establish the equivalence between the existence of optimal feedback operator for infinite dimensional stochastic linear quadratic control problems and the solvability of the corresponding operator-valued, backward stochastic Riccati equations. In order to handle the latter nonlinear equations, we adapt our stochastic transposition method, which was developed in our previous works but for operator-valued, backward stochastic (linear) Lyapunov equations.


Biography
Xu Zhang is a Cheung Kong Scholar Distinguished Professor of Mathematics at Sichuan University. He obtained a bachelor’s degree from Sichuan University in 1989, and a PhD degree from Fudan University in 1999. His main research interests include control theory, PDEs, and stochastic analysis. Professor Zhang is also a chief/associate editor of various journals, including SIAM J. Control Optim., ESAIM: COCV, Mathematical Control and Related Fields, etc. He has received a number of honors in his career, among which we mention his 2nd class award of Natural Science of China and 45-minute invited talk at the 2010 ICM.