Handling Structural Plant-model Mismatch using a Model-error Model in the Multi-stage NMPC framework

Abstract

Nonlinear model predictive control (NMPC) is one of the most promising advanced control approaches for multi-dimensional systems with state and input constraints. Among the several NMPC schemes that were proposed to deal with the uncertainties present in the model, the multi-stage NMPC approach achieves a low degree of conservatism because it incorporates the existence of recourse in the predictions. The future evolution of the state trajectories for different realizations of the uncertainty is modeled as a scenario tree. In this paper, we extend the multi-stage NMPC approach to deal with structural plant-model mismatch in a non-conservative fashion. An uncertainty region around the nominal model is built using a model-error model that consists of stable linear time-invariant dynamics and a static time-variant nonlinear mapping. The scenario tree is built for the nominal and for the extreme realizations of the plant obtained using the nominal model and the model-error model, and a multi-stage decision problem is formulated. We show the advantages of using a model-error model over a previously proposed approach to handle the structural plant model mismatch using multi-stage NMPC for a continuous stirred tank reactor (CSTR) example.