A Mini-Course on Stochastic Control

TL;DR

This paper provides a concise introduction to stochastic control theory, highlighting unique challenges and differences from deterministic control, especially in controllability and optimal control problems for stochastic differential equations.

Contribution

It offers an accessible overview of stochastic control issues, emphasizing new phenomena and difficulties distinct from deterministic systems, with illustrative examples.

Findings

Stochastic control problems differ significantly from deterministic ones.

Controllability and optimal control in stochastic systems present unique challenges.

Examples demonstrate the distinct formulation and solution methods for stochastic control.

Abstract

This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, we 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 counterpart.