Online learning‐based model predictive control with Gaussian process models and stability guarantees

• Published in: International journal of robust and nonlinear control Vol. 31; no. 18; pp. 8785 - 8812
• Main Authors: Maiworm, Michael, Limon, Daniel, Findeisen, Rolf
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.12.2021
• Subjects: Control stability; Data points; Distance learning; Gaussian process; Gaussian processes; input‐to‐state stability; Machine learning; online learning; Output feedback; Prediction models; Predictive control; recursive updates
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5361

Model predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled process is sufficiently accurate. One way to address this challenge is by data‐driven and machine learning approaches, such as Gaussian processes, that allow to refine the model online during operation. We present a combination of an output feedback model predictive control scheme and a Gaussian process‐based prediction model that is capable of efficient online learning. To this end, the concept of evolving Gaussian processes is combined with recursive posterior prediction updates. The presented approach guarantees recursive constraint satisfaction and input‐to‐state stability with respect to the model–plant mismatch. Simulation studies underline that the Gaussian process prediction model can be successfully and efficiently learned online. The resulting computational load is significantly reduced via the combination of the recursive update procedure and by limiting the number of training data points while maintaining good performance.