Title: Dynamical System Identification: An Operator Theoretic Approach

			Ben Recht
   Center for the Mathematics of Information
       California Institute of Technology

ABSTRACT: In this lecture, I will present a new algorithm for System
ID developed from the operator theoretic perspective that we explored
last week.  I will show how frequency and time domain observations can
be represented as linear functionals on systems.  I will then
demonstrate how find a stable, causal, and low-order linear system
satisfying such time and frequency domain constraints by minimizing a
particular norm on the space of linear systems.  This norm
approximates the McMillan degree function and is equivalent to the
nuclear norm of a special infinite dimensional operator which arises
in the study of model reduction.  The dual associated with minimizing
this norm subject to linear constraints is a finite dimensional
optimization problem that can be solved via semidefinite programming.
An optimal low-order linear system can then be constructed from a dual
optimal solution by solving a system of linear equations.  I will make
this algorithm concrete with several examples.