Recursive Gaussian Process Regression with Integrated Monotonicity Assumptions for Control Applications

TL;DR

The paper addresses online learning for control with Gaussian Processes while enforcing inequality constraints and monotonicity. It extends Recursive Gaussian Process (RGP) regression by adding soft inequality constraints via EKF pseudo-measurements and explicitly incorporating monotonicity through GP derivative information. The approach achieves real-time capability by computational load reductions, sequential EKF updates, and offline precomputations, and is validated both in simulations and experimentally on a vapor compression cycle evaporator with partial input-output linearization. Results show improved data efficiency and physically consistent behavior under limited data, highlighting the method's practical potential for safe, online control learning in thermal systems.

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).

Figures (6)

• Figure 1: Schematic illustration of the update heuristic.
• Figure 2: RGP and RGPm outputs in comparison with the hidden function $z$ after 5 time steps.
• Figure 3: Average RMSE for 500 simulation runs of the different RGP and RGPm variants.
• Figure 4: Average cumulative pseudo-measurement updates (CPMU) for 500 simulation runs of the different RGPm variants.
• Figure 5: Nonlinear tracking control structure.