Direct Data Driven Control Using Noisy Measurements

XX, XXXX 2017 1 Direct Data Driven Control Using Noisy Measurements Ramin Esmzad, Gokul S. Sankar, T eawon Han, Hamidreza Modares, Senior, IEEE 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. I NTRODUCTION D IRECT data-driven control has recently gained a surge of interest due to its control-oriented approach to solving control design problems [1]-[3]. That is, controller parameters are learned directly using input-output or input-state trajectories, without explicitly constructing a predictive model of the system. Bypassing system identification allows for leveraging the collected data to achieve what is best for the control objectives rather than using the data to fit a predictive model.