NMPC Through qLPV Embedding: A Tutorial Review of Different Approaches

Abstract Nonlinear Model Predictive Control (NMPC) formulations through quasi-Linear Parameter Varying (qLPV) embeddings have been brought to focus in recent literature. The qLPV realisation of the nonlinear dynamics yields linear predictions at each sampling instant. Thereby, these strategies generate online programs with reduced numerical burden, much faster to solve than the Nonlinear Programs generated with regular NMPC. The general lines of these methods: (i) The qLPV embedding is formulated with state-dependent scheduling parameters; (ii) Recursive extrapolation procedures are used to estimate the values of these parameters along the prediction horizon; (iii) These estimates are used to compute linear predictions, which are incorporated by the constrained optimisation procedure. This paper details the overall concept of these novel NMPC techniques and reviews two different (efficient) implementation options. Realistic academic examples are provided to illustrate their performances.