The Advanced Step Real Time Iteration for NMPC

This paper introduces an extension to the well-known Real Time Iteration (RTI) for Nonlinear Model Predictive Control (NMPC). We combine algorithmic ideas of the RTI, Advanced Step Controller and Multi-Level Iteration (MLI) framework and get thereby a family of new algorithms that allow one to trade control performance for computational efficiency in a flexible way. The main idea is to improve the linearization point for a new iteration by making cheap iterations with a new initial parameter prediction. We derive a general contraction estimate for the new algorithm and show that this approach yields closer tracking of the optimal solution manifold and results in better control performance. The efficacy of our approach is shown on a nontrivial numerical example.