This is a graduate course on mathematical theory of control and optimization, with a focus on geometric and topological methods.
A subset of the following topics will be covered:
Introduction to the basics of differential geometric, Riemannian geometry, algebraic topology and Lie group theory. Control systems on manifolds. Controllability and observability of nonlinear systems. Optimization on manifolds and Lie groups and their applications in signal processing and learning. Control of non-holonomic systems and mechanical systems, rigid body dynamics. Optimal control on manifolds and Lie groups. Feedback linearization and feedback invariants. Introduction to quantum control.
Instructors:
Prof. Baryshnikov, Prof. Belabbas.
Office hours (Baryshnikov): Fridays, noon-1pm (or by arrangement), on zoom.
Syllabus:
Class schedule is here. We will be using several texts, such as
Sontag’s Mathematical Control Theory, Agrachev and Sachkov’s Control Theory from the Geometric Viewpoint, and a few other (like Arnold’s Mathematical Methods).
Grading of the course will be based on the 4-5 homework assignments (70%) and a project (30%).