Stability properties of multi-stage nonlinear model predictive control

Abstract

This paper discusses the stability properties of a robust nonlinear model predictive control (NMPC) scheme that is based on a multi-stage optimization formulation. The use of a scenario tree to represent the uncertainty makes it possible to formulate a closed-loop robust approach with recourse which improves the open-loop approach in terms of performance and domain of attraction. We show that a straightforward formulation of a multi-stage NMPC scheme does not guarantee Input-to-State stability (ISS) in a deterministic setting, in contrast to the results that one gets using stochastic stability concepts. Since for many applications deterministic stability guarantees are desired, we provide an alternative formulation to achieve deterministic ISS and recursive feasibility guarantees for the case of discrete values of the uncertainty. The design and the performance of the proposed schemes are illustrated by simulations for a highly nonlinear example.