Learning-based Nonlinear Model Predictive Control * *The authors would like to ackowledge to the Spanish MINECO Grant PRX15-00300 and projects DPI2013-48243-C2-2-R and DPI2016-76493-C3-1-R as well as to the Engineering and Physical Research Council, grant no. EP/J012300/1 for funding this work.

Abstract

This paper presents stabilizing Model Predictive Controllers (MPC) in which prediction models are inferred from experimental data of the inputs and outputs of the plant. Using a nonparametric machine learning technique called LACKI, the estimated (possibly nonlinear) model function together with an estimation of Holder constant is provided. Based on these, a number of predictive controllers with stability guaranteed by design are proposed. Firstly, the case when the prediction model is estimated offline is considered and robust stability and recursive feasibility is ensured by using tightened constraints in the optimisation problem. This controller has been extended to the more interesting and complex case: the online learning of the model, where the new data collected from feedback is added to enhance the prediction model. An on-line learning MPC based on a double sequence of predictions is proposed.