Data-Driven Control under Input and Measurement Noise

Event Status
Scheduled
Jared Miller

Data-Driven Control (DDC) is a methodology that formulates controllers directly from observations without requiring a system identification step. DDC under process noise can be achieved in polynomial time (under assumptions on noise structure) through methods such as Subspace Methods, Willem’s Fundamental Lemma, Superstability, and Quadratic Matrix Inequalities. The introduction of input and measurement noise is called the Error-in-Variables (EIV) setting, and adds a bilinearity that results in NP-hard system identification and control problems. This work presents a polynomial-optimization based framework to perform stabilizing and robust control of all consistent plants in the EIV setting when all noise processes are L-infinity norm bounded. The moment-Sum-of-Squares (SOS) hierarchy is used to find a superstabilizing or quadratically stabilizing common controller, where each nonnegativity constraint is posed over the set of unknown plants and unknown noise processes. A theorem of alternatives is used to eliminate the unknown noise variables and improve computational scalability. This SOS-based framework may be extended towards the control of autoregressive models with input-output data.


 

Date and Time
April 10, 2023, 11 a.m. to noon
Location
POB 6.304