TEXT: Curtain and Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer-Verlag, 1995, ISBN 0387944753.
Prerequisites: Linear Systems (new number AMES 280A) or consent of instructor
Course Objective: This is a research-oriented course which is this year motivated by current activities at UCSD on control of flows and flexible structures. The course will focus on the most basic questions in system theory for infinite-dimensional systems such as characterization of solutions, controllability, and stabilizability (the dual questions of observability and detectability will be deemphasized). The objective will not be to cover the most up-to-date methods for control design (optimal, robust, etc) for infinite-dimensional linear systems, but rather to prepare the students for posing and answering design questions in the open area of control of nonlinear infinite-dimensional systems. While infinite-dimensionality can be created by many phenomena including pure delays, the focus of the course will be on applications to partial differential equations. As this is a course on a relatively unestablished subject, the level will be informal and the pace will be highly dependent on the student's participation. Teaching responsibilities will be shared between Prof. Krstic and Drs. Balogh and Liu.
Topics: Strongly continuous semigroups, infinitesmal generators, unbounded closed linear operators, Hille-Yosida theorem, Riesz-spectral operators. Existence and uniqueness of solutions of abstract evolution equations, pertubation and composite systems. Boundary control systems. Controllability, exact and approximate, Hilbert uniqueness method, fixed point method. Input-output maps, transfer functions. Exponential stability, stabilizability, Lyapunov equation. Controllability via stabilizability. Compensator design.