GEOMETRY, TOPOLOGY AND CONTROL SYSTEM DESIGN: Proceedings of a Banff International Research Station Workshop

This volume brings together 17 original research papers in mathematical control theory, rooted in the themes of the ”Geometry, Topology, and Control System Design” workshop held at the Banff International Research Station (BIRS) in June 2023 and organized by Mohamed Ali Belabbas (University of Illinois, Urbana-Champaign), Anthony Bloch (University of Michigan), Xudong Chen (Washington University), Monique Chyba (University of Hawaii), and Angelia Nedich (University of Arizona). The collection provides a valuable look into the current state of the field, showcasing a diverse range of methods and applications.
The contributions address a spectrum of contemporary and foundational problems. Key themes explored by the authors include:
● The fundamental challenges of feedback stabilization and controllability for ensemble systems, nonlinear dynamics, and discrete-time systems.
● The application of geometric, function analytic, and Lie-theoretic methods to problems involving singular arcs, invariant control systems, and time-dependent vector fields.
● The growing interface between control theory and data-driven analysis, with papers on deep learning, covariance steering, and the control of systems from data snapshots and unknown dynamics.
● The study of Markov processes and network interactions through the lens of divergence metrics and probabilistic methods.

This volume also stands as a tribute to the late Professor Roger Brockett, whose work is a cornerstone of the field. He passed away as the workshop was being organized, and his intellectual legacy is a unifying thread throughout the collection. The book opens with a chapter by Mohamed Ali Belabbas and John Baillieul, providing a brief and biased tour of his extensive and influential contributions. Many of the subsequent papers are also dedicated to his memory by their authors.