Fall 2011, Geometric Control Theory (formal title "Seminar in Geometry"), Math 666

The course is devoted to the modern Geometric Control Theory. This area is in the intersection of several fields of Mathematics such as Dynamical Systems, Calculus of Variation, Differential Geometry, and Theoretical Mechanics (but you do not need to have any preliminary background in any of these fields to take the course) and it has a lot of applications in Engineering and Physics. The course is intended both for mathematicians and for engineers. It consists of mainly three parts: Controllability, Optimal Control, and State-Feedback equivalence problems (the latter if the time permit). I will develop several powerful modern tools (such as Chronological Calculus) which will allow to move quickly from the foundations to the front of the current research in the field. The theory will be demonstrated on many practical examples such as car and trailer parking, control of rigid body (of a space craft), control of configurations (like a falling cat), and various optimal control problems of practical interest (e.g. fastest stop of the train, optimal control of a linear oscillator and others). I expect that a student will be ready to start a research project in the field after this course.

(a correction: on the first page of the solution when checking GPC the first component of Ab should be -11 and det (b, Ab)=-9)

Topics for the project and information about final exam and project presentations