2025/05/09 by Ramin Esmzad, Gokul S. Sankar, Esmzad, Ramin +5
Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Robotics (cs.RO) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2505.06407
openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.