Unconstrained feedback controller design using Q-learning from noisy data

This paper develops a novel model-free Q-learning based approach to estimate linear, unconstrained feedback controllers from noisy process data. The proposed method is based on an extension of an available approach developed to estimate the linear quadratic regulator (LQR) for linear systems with full state measurements driven by Gaussian process noise of known covariance. First, we modify the approach to treat the case of an unknown noise covariance. Then, we use the modified approach to estimate a feedback controller for linear systems with both process and measurement noise and only output measurements. We also present a model-based maximum likelihood estimation (MLE) approach to determine a linear dynamic model and noise covariances from data, which is used to construct a regulator and state estimator for comparisons in simulation studies. The performances of the model-free and model-based controller estimation approaches are compared with an example heating, ventilation, and air-conditioning (HVAC) system. We show that the proposed Q-learning approach estimates a reasonably accurate feedback controller from 24 h of noisy data. The controllers estimated using both the model-free and model-based approaches provide similar closed-loop performances with 3.5 and 2.7% losses respectively, compared to a perfect controller that uses the true dynamic model and noise covariances of the HVAC system. Finally, we give future work directions for the model-free controller design approaches by discussing some remaining advantages of the model-based approaches.