An Introduction to Stochastic Linear-Quadratic Optimal Control Problems
Stochastic linear-quadratic (LQ) control is one of the most fundamental and useful tools in modern engineering and finance and has developed into a major research area in control theory. It concerns linear systems driven by Brownian motions and aims to determine a control process that is optimal in the sense of minimizing the expected value of a quadratic cost criterion. In this talk, I will introduce two basic types of controls: open-loop control and state-feedback control generated by closed-loop strategy. I will discuss their advantages and disadvantages and present characterizations for both open-loop optimal controls and closed-loop optimal strategies. Then I will talk about the connections between open-loop and closed-loop solvabilities and further develop a scheme for finding near optimal state-feedback controls. This is a joint work with Professor Jiomgmin Yong.