Constrained Gaussian Process Learning for Model Predictive Control

TL;DR

This paper introduces a method using Gaussian processes within model predictive control to learn and guarantee the trackability of reference signals from noisy data, ensuring stability and performance in control tasks.

Contribution

It proposes a novel approach to incorporate Gaussian process learning with constrained hyperparameter optimization to guarantee reference trackability in MPC.

Findings

Effective learning of reference signals from noisy data.

Guarantees of trackability through constrained hyperparameter tuning.

Application to asymptotically constant and periodic references.

Abstract

Many control tasks can be formulated as a tracking problem of a known or unknown reference signal. Examples are movement compensation in collaborative robotics, the synchronisation of oscillations for power systems or reference tracking of recipes in chemical process operation. Tracking performance as well as guaranteeing stability of the closed loop strongly depends on two factors: Firstly, it depends on whether the future desired tracking reference signal is known and, secondly, whether the system can track the reference at all. This paper shows how to use machine learning, i.e. Gaussian processes, to learn a reference from (noisy) data, while guaranteeing trackability of the modified desired reference predictions in the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimization. Two specific scenarios, i.e. asymptotically constant and periodical references, are discussed.