2016/03/15 by Christian Feller, Feller, Christian, Christian Ebenbauer +1
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1603.04605
openalex publication_date 2016/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose and analyze a stabilizing iteration scheme for the algorithmic\nimplementation of model predictive control for linear discrete-time systems.\nPolytopic input and state constraints are considered and handled by means of\nso-called relaxed logarithmic barrier functions. The required on-line\noptimization is based on warm starting and performs only a limited, possibly\nsmall, number of optimization algorithm iterations between two consecutive\nsampling instants. The optimization algorithm dynamics as well as the resulting\nsuboptimality of the applied control input are taken into account explicitly in\nthe stability analysis, and the origin of the resulting overall closed-loop\nsystem, consisting of state and optimization algorithm dynamics, is proven to\nbe asymptotically stable. The corresponding constraint satisfaction properties\nare also analyzed. The theoretical results and a presented numerical example\nillustrate the fact that asymptotic stability as well as a satisfactory\nclosed-loop performance can be achieved by performing only a single\noptimization algorithm iteration at each sampling step.\n