Mixed–-Level Iteration Schemes for Nonlinear Model Predictive Control

In general, numerical schemes for nonlinear model predictive control (NMPC) require the (approximate) solution of a nonlinear program in each sample for feedback generation. Thus, the application of NMPC to processes that need fast feedback poses a major computational challenge. Recently, new multi–level iteration schemes have been proposed, extending the well–known idea of real–time iterations. These algorithms take into account different time scales inherent in the dynamic model by updating the data of the feedback–generating quadratic program (QP), i.e., Hessians and Jacobians, gradients, and constraint residuals, on different levels. In this contribution we consider new mixed–level updates of the QP data, which interval–wise apply different update levels. In particular, we apply higher–level updates more frequently on the first intervals of the control horizon, given their importance in the context of model predictive control in general. Targeting at modern computers with multi–core processing units, we describe an efficient parallel implementation of the mixed–level iteration approach and apply it to a benchmark problem from automotive engineering.