ECE 557

Graduate course on mathematical theory of control and optimization, with a focus on geometric and topological methods. 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. Course Information: 4 graduate hours. No professional credit. Prerequisite: ECE 515 or equivalent is required. A course on state-space control theory, multivariable calculus, linear algebra and overall mathematical maturity are recommended.