Automated Data-Driven Tuning of Learning-Based Model Predictive Control (SelfMPC): A Maximum-Likelihood Approach

The practical implementation of Model Predictive Control (MPC) often presents challenges that remain unaddressed in theoretical formulations. Among these challenges, the tuning of the receding horizon cost becomes particularly intricate in the context of data-driven learning-based MPC, where models exhibit partial uncertainty. This paper introduces SelfMPC, a pioneering approach within a Gaussian process learning framework, illustrating that a tracking MPC cost can be formulated as the maximum likelihood estimation of the reference output. This formulation provides automatic cost shaping and effective regularization, eliminating the need for manual tuning efforts. Moreover, the proposed formulation provides a natural way to employ information from empirical experiments into the definition of the MPC optimization problem for unknown systems. Empirical validation against conventional weighting matrix selection methods confirms the effectiveness of the proposed approach.