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Nonlinear MPC: the Impact of Sampling on Closed Loop Stability
Author(s) -
Worthmann Karl,
Reble Marcus,
Grüne Lars,
Allgöwer Frank
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410436
Subject(s) - model predictive control , control theory (sociology) , discretization , stability (learning theory) , nonlinear system , sampling (signal processing) , mathematical proof , mathematics , sampling time , exponential stability , computer science , control (management) , statistics , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , machine learning , filter (signal processing) , computer vision
In this paper we consider model predictive control (MPC) schemes without stabilizing terminal constraints and/or costs for continuous time systems. While the estimates on the required prediction horizon length such that asymptotic stability of the MPC closed loop is guaranteed yield, in general, satisfactory results their applicability is limited due to the fact that the respective proofs assume that the input function can be switched arbitrarily often on compact time intervals. We present a technique which allows to determine a suitable discretization accuracy such that the obtained performance bound is preserved while the control signal is only switched at the sampling instants of the corresponding sampled data system. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)