Contraction Properties of the Advanced Step Real-Time Iteration for NMPC⁎This research was supported by the German Federal Ministry of Education and Research (BMBF) via the funded Kopernikus project: SynErgie (03SFK3U0) and by the German Federal Ministry for Economic Affairs and Energy (BMWi) via eco4wind (0324125B) and DyConPV (0324166B), and by DFG via Research Unit FOR 2401. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Nurkanović, Armin; Zanelli, Andrea; Albrecht, Sebastian; Frison, Gianluca; Diehl, Moritz
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 7041
• Page End: 7048
• Publication Date: 2020
• Subjects: nonlinear model predictive control -- numerical methods -- nonlinear optimization; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.449
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper we study the contraction properties of the recently introduced Advanced Step Real-Time Iteration (AS-RTI) under active-set changes. Compared to the well-known Real-Time Iteration, in order to improve optimality, in the AS-RTI some extra calculations on a problem with a predicted state are carried out. This enables us to trade off controller performance for computational load in a simple manner. Under standard assumptions, we prove the contraction of the iterates and boundedness of the numerical error. To achieve these goals we use generalized equations, Robinson's strong regularity and recently presented results for abstract real-time algorithms. Finally, we present a numerical benchmark, where the performance of different variants of the AS-RTI is demonstrated on an industrial case study.