Data-Driven Linear Quadratic Control Using Output-Feedback via Non-Minimal Realization

TL;DR

This paper introduces a data-driven output-feedback control method for unknown linear systems using non-minimal realization and adaptive dynamic programming, enabling optimal control from input-output data.

Contribution

It develops a novel output-feedback learning framework based on a non-minimal realization and value iteration, achieving optimal control without knowing system matrices.

Findings

The optimal gain of the augmented system recovers the original optimal gain.

The proposed method is implementable from input-output data.

Simulation results validate the controller's performance.

Abstract

In this paper, we investigate a continuous-time linear quadratic control problem for systems with unknown matrices, where only input-output data are available. We propose an output-feedback learning framework based on a canonical nonminimal realization constructed through Kreisselmeier's adaptive filter. The filter admits an observer interpretation, which leads to an augmented system that preserves the input-output response of the realization and provides accessible state trajectories. We show that the optimal gain of this augmented system explicitly recovers the optimal gain associated with the canonical non-minimal realization, and hence achieves the optimal state-feedback solution of the original plant. Exploiting this relation and the known structure of the augmented input matrix, we develop a data-driven value iteration algorithm within the adaptive dynamic programming framework. The resulting controller is implementable from input-output data, and its performance is validated via simulations.