Direct Data Driven Control Using Noisy Measurements

2025-05-09

AI Summary

This paper addresses the problem of designing an LQR controller directly from a single batch of noisy input-output data for an unknown linear system, bypassing explicit system identification. The proposed method is purely data-driven and integrates statistical noise modeling with direct controller synthesis. Its key contributions are threefold: (i) it establishes, for the first time, a theoretical link between mean-square stability of the data-driven closed-loop system and stability of the true (unknown) system; (ii) it derives a robust stability criterion formulated as a linear matrix inequality (LMI), and constructs an optimal controller synthesis framework cast as a semidefinite program (SDP), ensuring both mean-square stability and optimality of the steady-state covariance; and (iii) it requires no prior knowledge of system structure or exact noise distribution. The approach is validated on benchmark systems—including the rotational inverted pendulum and active suspension—demonstrating superior robustness and control accuracy compared to existing data-driven LQR methods.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Solving LQR with unknown dynamics and noisy measurements
• Bypassing system identification using noisy input-output data
• Ensuring stability and optimal performance via convex optimization

Innovation

• Direct data-driven control bypassing system identification
• Convex optimization incorporating noise statistics
• LQR solution via semidefinite programming (SDP)