Thesis Defense: Finite Time System Identification from Noisy Data

THESIS COMMITTEE:

Prof. Munther A. Dahleh (Thesis Supervisor)

Prof. Yury Polyanskiy

Prof. Alexander Rakhlin

Dr. Mardavij Roozbehani

 

This thesis develops statistical tools and algorithmic techniques for non-asymptotic system identification of dynamical systems from noisy input-output data. Specifically, we address the question: “For a fixed length of noisy data generated by an unknown model, what is the best approximation that can be estimated?”; this is in contrast to traditional system identification which answers the question of estimating the unknown model when data length tends to infinity. In this sense, non–asymptotic results are more difficult to derive but more applicable in the context of control, robotics and reinforcement learning.

 

We show how to extract lower-dimensional approximations of the underlying system directly from noisy data; in contrast to the traditional model reduction where complete knowledge of the true system is required to obtain low order approximations. This is achieved by a data-dependent rule that outputs an order approximation which grows as a function of the data length. Finally, we compare our algorithm to other standard approaches.