Multistage NMPC with model-error model

This paper proposes and evaluates new schemes for robust nonlinear model predictive control (NMPC) in the presence of unstructured (non-parametric) model uncertainty. The approach builds on the concept of model-error models (MEM) which bound the possible dynamics of the error between the nominal model and the real system. The MEM are integrated into multi-stage NMPC formulations. Among the various robust NMPC schemes, multi-stage NMPC achieves a low degree of conservatism by incorporating future reactions of the controller when new measurements become available in its predictions using a scenario tree with recourse variables. The scenario tree describes a set of possible behaviours of the plant, usually by assuming different (e.g., minimum, maximum, nominal) values of some parameters of the plant model. However, in reality there is always unstructured plant-model mismatch due to, for example unmodelled dynamics or simplified model equations. The existing robust NMPC schemes handle structural plant-model mismatch only by embedding it in additive uncorrelated disturbances. It has been shown in linear control theory that dynamic MEM can significantly reduce the conservatism of roust control formulations. Here the scenario tree is constructed using the nominal model and the MEM to represent the non-parametric dynamic plant-model mismatch. The resulting computational burden of the multi-stage approach is reduced by introducing two different simplified formulations, constraint tightened multi-stage NMPC with MEM and tube-enhanced multi-stage NMPC with MEM. The proposed schemes are evaluated using examples from the chemical engineering field.