Recursive Gaussian Process Regression with Integrated Monotonicity Assumptions for Control Applications

TL;DR

This paper introduces a recursive Gaussian Process regression method that incorporates inequality constraints and monotonicity assumptions, enabling real-time control applications with improved performance and computational efficiency.

Contribution

It extends recursive Gaussian Process regression to include inequality constraints and monotonicity, optimized for real-time control tasks with low computational overhead.

Findings

Validated through simulations showing advantages over standard RGP

Demonstrated real-time applicability in control of heat transfer in a vapor cycle

Achieved monotonicity preservation in practical control scenarios

Abstract

In this paper, we present an extension to the recursive Gaussian Process (RGP) regression that enables the satisfaction of inequality constraints and is well suited for a real-time execution in control applications. The soft inequality constraints are integrated by introducing an additional extended Kalman Filter (EKF) update step using pseudo-measurements. The sequential formulation of the algorithm and several developed heuristics ensure both the performance and a low computational effort of the algorithm. A special focus lies on an efficient consideration of monotonicity assumptions for GPs in the form of inequality constraints. The algorithm is statistically validated in simulations, where the possible advantages in comparison with the standard RGP algorithm become obvious. The paper is concluded with a successful experimental validation of the developed algorithm for the monotonicity-preserving learning of heat transfer values for the control of a vapor compression cycle evaporator, leveraging a previously published partial input output linearization (IOL).