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On quadratic stage costs for mobile robots in model predictive control
Author(s) -
Müller Matthias A.,
Worthmann Karl
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710380
Subject(s) - model predictive control , control theory (sociology) , terminal (telecommunication) , quadratic equation , horizon , stability (learning theory) , mathematical optimization , quadratic programming , mobile robot , finite set , optimal control , computer science , nonholonomic system , control (management) , mathematics , robot , artificial intelligence , telecommunications , mathematical analysis , geometry , machine learning
Abstract We consider nonholonomic mobile robots. Since the system is finite time controllable, it is stabilizable by a receding horizon control scheme with purely quadratic stage costs if an infinite optimization horizon is employed. However, due to the so called short‐sightedness of model predictive control, these stability properties are not preserved if the control problem is only optimized on a truncated and, thus, finite prediction horizon — even if an arbitrarily large terminal weight is added. Hence, it is necessary to either incorporate structurally different terminal costs or use non‐quadratic stage costs to appropriately penalize the deviation from the desired set point. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)