Geometric and Analytic Facets of Feedback Design: Control Theory Meets Policy Optimization and Modern Applications

Abstract

This talk is motivated by applications that require a new perspective on elementary control/filter design and algorithms. In particular, I will motivate why in certain scenarios, it becomes important to relax the knowledge of exact parameterization of the system, noise statistics, and/or disturbances, in order to develop feedback control and filters. As a guiding example, I will consider clock synchronization in satellite constellations, which is essential for positioning, navigation, and timing. This application highlights the need for filtering techniques that do not rely on precise knowledge of noise and measurement covariances. Building on this motivation, I will then step back and introduce a calculus for control and filter design based on direct policy optimization using first-order methods, while revisiting several outstanding problems in control. The goal of this plenary is to highlight key analytic and geometric features of this perspective on system design and provide pointers to some of the ongoing efforts in this rapidly growing area.