Direct Integration of Recursive Gaussian Process Regression Into Extended Kalman Filters With Application to Vapor Compression Cycle Control

Abstract

This paper presents a real-time capable algorithm for the learning of Gaussian Processes (GP) for submodels. It extends an existing recursive Gaussian Process (RGP) algorithm which requires a measurable output. In many applications, however, an envisaged GP output is not directly measurable. Therefore, we present the integration of an RGP into an Extended Kalman Filter (EKF) for the combined state estimation and GP learning. The algorithm is successfully tested in simulation studies and outperforms two alternative implementations -- especially if high measurement noise is present. We conclude the paper with an experimental validation within the control structure of a Vapor Compression Cycle typically used in refrigeration and heat pumps. In this application, the algorithm is used to learn a GP model for the heat-transfer values in dependency of several process parameters. The GP model significantly improves the tracking performance of a previously published model-based controller.