Dual Control in Big Data Era: An Overview

This paper provides an overview of dual control and its applications in the big data era. Different non-dual and dual controllers as well as their attributes, complexity, and limitations are analyzed. As an example, dual control of a class of discrete-time LQG problems with unknown parameters in both the state and observation equations is discussed in depth. Optimal dual control, openloop feedback control, active open-loop feedback control via variance minimization approach, and optimal nominal dual control are demonstrated for this type of problems. The optimal nominal dual control, taking into account the effect of future learning, is the best possible (partial) closed-loop feedback control that can be achieved. Applications of dual control in economic systems, manufacturing processes, information retrieval, robotics, etc. are also introduced.