Monday,
April 9, 1:30 p.m. GWC 409
Robert C. Thompson
School of Mathematical and Statistical Sciences
System Identification via Basis Pursuit (MS defense)
Abstract
We consider the application of basis pursuit to several problems in system identification. After reviewing some key results in the theory of basis pursuit and compressed sensing, we describe numerical experiments that explore the application of basis pursuit to the black-box identification of linear time-invariant (LTI) systems with both finite (FIR) and infinite (IIR) impulse responses, temporal systems modeled by ordinary differential equations, and spatio-temporal systems modeled by partial differential equations. For LTI systems, our experimental results illustrate existing theory for identification of LTI FIR systems. We find that basis pursuit does not identify sparse LTI IIR systems, but it does identify alternate systems with identical response characteristics when there are small numbers of non-zero coefficients. For ODE systems, our experimental results are consistent with earlier research for differential equations that are polynomials in the system variables, illustrating feasibility of the approach for small numbers of non-zero terms. For PDE systems, we find that basis pursuit can be applied to system identification, and compare performance with another existing method. In all cases the impact of measurement noise on identification performance is considered, and we empirically observe that high signal-to-noise ratio is required for successful application of basis pursuit to system identification problems.
