Robust Multi-Stage Nonlinear Model Predictive Control Using Sigma Points

Abstract

We address the question of how to reduce the inevitable loss of performance that is incurred by robust multi-stage NMPC due to the lack of knowledge compared to the case where the exact plant model (no uncertainty) is available. Multi-stage NMPC in the usual setting over-approximates a continuous parametric uncertainty set by a box and includes the corners of the box and the center point into the scenario tree. If the uncertainty set is not a box, this augments the uncertainty set and results in a performance loss. In this paper, we propose to mitigate this problem by two different approaches where the scenario tree of the multi-stage NMPC is built using sigma points. The chosen sigma points help to capture the true mean and covariance of the uncertainty set more precisely. The first method computes a box over-approximation of the reachable set of the system states whereas the second method computes a box over-approximation of the reachable set of the constraint function using the unscented transformation. The advantages of the proposed schemes over the traditional multi-stage NMPC are demonstrated using simulation studies of a simple semi-batch reactor and a more complex industrial semi-batch polymerization reactor benchmark example.