Online Gaussian Process learning-based Model Predictive Control with Stability Guarantees

Model predictive control provides high performance and safety 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 of sufficient accuracy. 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 a output feedback model predictive control scheme, which does not require full state information, and a Gaussian process prediction model that is capable of online learning. To this end the concept of evolving Gaussian processes is combined with recursively updating the posterior prediction. The presented approach guarantees input-to-state stability w.r.t. to the model-plant mismatch. Extensive simulation studies show that the Gaussian process prediction model can be successfully learned online. The resulting computational load can be significantly reduced via the combination of the recursive update procedure and limiting the number of training data points, while maintaining performance at a comparable level.