Abstract: In this talk, I will give a short introduction to control theory of stochastic distributed parameter systems (governed by stochastic differential equations in infinite dimensions, typically by stochastic PDEs). I will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, I will show by some examples that both the formulation of stochastic control problems and the tools to solve them may differ considerably from their deterministic/finite-dimensional counterparts.
Xu Zhang 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.