Learning-Enabled Robust Control with Noisy Measurements

TL;DR

This paper introduces a novel adaptive control method for linear systems with uncertain parameters, utilizing dynamic programming and information states to achieve robust performance despite noisy measurements.

Contribution

It presents a constructive, finite-dimensional approach to bounded $ ext{l}_2$-gain adaptive control without requiring prior stabilizing controllers.

Findings

Successfully constructs an information state using $ ext{H}_ ext{infty}$-observers.

Provides a recursive method to compute performance metrics.

Achieves robust control with noisy measurements for uncertain systems.

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.