Learning-Enabled Robust Control with Noisy Measurements

Abstract

We present a constructive approach to bounded ${\ell }_2$-gain adaptive control with noisy measurements for linear time-invariant scalar systems with uncertain parameters belonging to a finite set. The gain bound refers to the closed-loop system, including the learning procedure. The approach is based on forward dynamic programming to construct a finite-dimensional information state consisting of ${\mathcal{H}}_{\infty }$-observers paired with a recursively computed performance metric. We do not assume prior knowledge of a stabilizing controller.

Submitted to L4DC 2022