Multi-stage Nonlinear Model Predictive Control with verified robust constraint satisfaction

This paper presents an approach to verify robust constraint satisfaction using dynamic state bounding techniques in the framework of multi-stage Nonlinear Model Predictive Control (NMPC). In multi-stage NMPC, the uncertainty is described by a tree of discrete scenarios, and the future control inputs depend on the previous realizations of the uncertainty, constituting a closed-loop approach which has been shown to provide significantly better performance than an open-loop approach. While the approach has demonstrated very promising results in practice, one of the problems of multi-stage NMPC is the fact that no guarantees can be given for the uncertainty values that are not explicitly considered in the scenario tree. In this work, we address this problem by updating the resulting optimization problem in an iterative fashion such that the constraints satisfaction is guaranteed based on the rigorous bounding of the state variables over the set of possible uncertainty realizations. We illustrate that the approach can deal in real time with challenging problems by presenting simulation results of an industrial batch polymerization reactor.