Enforcing Soft Monotonicity Constraints for Recursive Gaussian Process Regression in Real Time

In this work, we introduce a real-time capable algorithm for considering monotonicity assumptions for recursive Gaussian Process regression (RGP). Therefore, we present how to efficiently calculate the RGP gradients online. Then, we utilize an extended Kalman filter and pseudo-measurements in combination with a ReLU pseudo-measurement function to enforce soft inequality constraints. This work builds upon a previously published conference paper with the same goal and a similar fundamental approach. Opposite to our previous work, however, we now use an exact covariance calculation for the RGP gradients. Furthermore, we also present a real-time optimized version of this algorithm with less simplifications compared to the previously published version. These and several other algorithmic innovations lead to an algorithm with greatly improved numerical robustness. The algorithm is validated and compared to its previously published version for a 2D numerical example. The paper is concluded with a successful experimental validation of the developed algorithm for the monotonicity-preserving learning of pneumatic valve characteristics for the control of a pneumatic system, leveraging a partial input - output linearization.