Latent variable based model predictive control: Ensuring validity of predictions

This paper presents a methodology to constrain the optimisation problem in LV-MPC so that validity of predictions can be ascertained. LV-MPC is a model-based predictive control methodology implemented in the space of the latent variables and is based on a linear predictor. Provided real processes are non-linear, there is model-process mismatch, and under tight control, the predictor can be used for extrapolation. Extrapolation leads to bad predictions which deteriorates control performance, hence the interest in validity of predictions. In the proposed approach first two validity indicators on predictions are defined. The novelty in the two indicators proposed is they neglect past data, and so validity of predictions is ascertained in terms of future moves which are actually the degrees of freedom in the optimisation. Second, the indicators are introduced in the optimisation as constraints. Provided the indicators are quadratic, recursive optimisation with linearised constraints is implemented. A MIMO example shows how ensuring validity of predictions neglecting past data can improve closed-loop performance, specially under tight control outside the identification region.