Direct Data Driven Control Using Noisy Measurements

TL;DR

This paper introduces a new data-driven control method for LQR problems that works directly with noisy measurements, ensuring stability and optimality without system identification, demonstrated through simulations on benchmark systems.

Contribution

It develops a robust, noise-aware data-driven LQR framework that guarantees stability and optimality using convex optimization, bypassing system identification.

Findings

Guarantees mean-square stability with noisy data

Provides a convex optimization-based controller synthesis method

Demonstrates superior robustness in simulations

Abstract

This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems -- including a rotary inverted pendulum and an active suspension system -- demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible.