Learning and information for dual control

In dual control problems, the aim is to concurrently learn and control an unknown system. However, actively learning the system conflicts directly with any given control objective as it involves disturbing the system for exploration. This paper presents a multi-objective approach to dual control, which explicitly quantifies both the learning and control objectives. Mutual information and relative entropy from information theory are used to quantify the information gain in active learning as part of the exploration process. The information gain is then balanced against a standard control objective. The presented approach is illustrated using Gaussian process regression, which provides a framework for learning nonlinear systems and is used as a demonstrative example. It is shown that the derived information measures are closely related to the variance of the predictive Gaussian distribution estimating the system.