Online learning-based Model Predictive Control with Gaussian Process Models and Stability Guarantees
This work addresses the problem of ensuring safety and performance in control systems for applications like robotics or autonomous vehicles, but it is incremental as it builds on existing MPC and GP methods.
The paper tackles the challenge of maintaining accurate models for model predictive control by combining an output feedback MPC scheme with an online-learning Gaussian process model, achieving recursive constraint satisfaction and input-to-state stability while reducing computational load through efficient data handling.
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.