Minimum Information Control: Theory, Applications, and Recent Progress

Abstract: Control theory is a branch of information science studying the use of feedback to make real-time decisions in order to achieve a desired goal. The advantage of feedback control over open-loop control is widely recognized. In many modern control systems, however, processing the sheer wealth of information available for decision-making can become cumbersome, imperiling efficient real-time processing. Likewise, transmitting measurements over communication networks uses scarce physical resources (like time, bandwidth, and power) that could otherwise be allocated to other devices and services. Consequently, the ability to select only the essential, task-relevant information from the vast sea of sensory data is increasingly relevant. This leads to a series of non-trivial questions at the boundary between control theory and information theory: What is the minimum amount of information to be fed back to keep making sensible decisions? What information needs to be fed back? How do we quantify the amount of information that is fed back?

In this talk, we introduce an approach to quantifying the flow of feedback information using an information-theoretic concept known as directed information. Following a brief historical overview of directed information, we employ it to formulate the concept of minimum information control. We elucidate the practical relevance of this problem formulation by demonstrating its natural emergence in Networked Control Systems (NCS) design problems. We will also showcase the utility of minimum information control in path planning and sensor selection problems.