On stochastic PDE control

In this talk, I will give a short introduction to control theory for stochastic distributed parameter systems (governed by stochastic differential equations in infinite dimensions, typically by stochastic PDEs). I will explain the new phenomena and difficulties in the study of controllability and optimal control problems for these sorts of equations. In particular, I will show by some examples that both the formulation of corresponding stochastic control problems and the tools to solve them may differ considerably from their deterministic/finite-dimensional counterparts, and one has to develop new methods, say, the stochastic transposition method introduced in our previous works, to solve some problems in this field.