Errors-in-Variables Data-Driven Receding-Horizon LQR

Abstract

This letter addresses the data-driven linear quadratic regulator (LQR) problem with input constraints under process noise and errors-in-variables measurement errors. Using noisy state and input measurements, we design controllers that ensure closed-loop stability, minimize a quadratic cost, and respect input bounds without identifying the system dynamics. The problem is formulated as a robust polynomial optimization over all models consistent with the data and noise bounds. By applying the theorem of alternatives and sum-of-squares techniques, we derive tractable certificates that eliminate the measurement-error variables, reducing the complexity of the resulting relaxations. Two formulations are proposed: a matrix-valued formulation based on Scherer’s Positivstellensatz and a scalarized alternative enabling Putinar-type certificates.