Potential and Limitations of Multi-stage Nonlinear Model Predictive Control

Abstract

Multi-stage Nonlinear Model Predictive Control (NMPC) is a promising strategy for the design of robust NMPC controllers which is based on describing the evolution of the uncertainty as a scenario tree. The scenario tree makes it possible to consider explicitly that the future control inputs can be adapted to the future information (measurements), thus reducing the conservativeness of the robust approach. This paper reviews the multi-stage approach and illustrates its main advantages using a nonlinear CSTR example. We also provide guidelines for possible multi-stage NMPC users that could help to identify the problems where the use of multi-stage NMPC can result in a significant improvement with respect to standard NMPC or other robust NMPC approaches. Finally, we summarize the different modifications that can be done to the multi-stage approach to enhance its performance. The possible enhancements include: improved performance using parameter estimation, rigorous guarantee of constraint satisfaction, and stability guarantees for the case of discrete-valued uncertainties.