Harald Aschemann

Ricus Husmann, Sven Weishaupt, Harald Aschemann

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.

Ricus Husmann, Sven Weishaupt, Malin Lotta Husmann et al.

In this paper, we present a learning-based control for a class of nonlinear systems that guarantees exponential stability as well as bounded output errors. The control is based on the Gaussian Process Submodel Online Learning (GPSOL) algorithm and the Disturbance Error Rate Limiting (DERL) algorithm, both of which were developed in previous work. The GPSOL algorithm provides a method to learn Gaussian Process (GP) models for subsystems online, whereas the DERL algorithm allows to limit the rate of the prediction error of these GP models. The focus of this paper is the utilization of the GP model within an adaptive controller and the derivation of corresponding stability conditions and system peak-to-peak gains by means of linear matrix inequalities (LMIs). These peak-to-peak gains are then used to prescribe a desired prediction error rate for the DERL algorithm to achieve user-defined output error bounds. The gains and the related bounds were successfully verified using a simulation model. Furthermore, results form a successful experimental validation of the bounds and the overall control structure on a pneumatic test rig are presented. While the control scheme and error bounds proposed in this paper are limited to first-order single-input-single-output systems, an extension to certain classes of higher-order and multiple-input-multiple-output systems is expected to be forthcoming.