Constrained Gaussian Process Learning for Model Predictive Control⁎⁎The work of this paper is supported by the Federal Ministry of education and Research within the Forschungscampus STIMULATEunder grant number ‘13GW0095A’.

Many control tasks can be formulated as tracking problems of a known or unknown reference signal. examples are motion compensation in collaborative robotics, the synchronisation of oscillations for power systems or the reference tracking of recipes in chemical process operation. Both the tracking performance and the stability of the closed-loop system depend strongly on two factors: Firstly, they depend on whether the future reference signal required for tracking 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 within the framework of model predictive control. Guarantees are provided by adjusting the hyperparameters via a constrained optimisation. Two specific scenarios, i.e. asymptotically constant and periodic REFERENCES, are discussed.