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Distributed and boundary model predictive control for the heat equation
Author(s) -
Altmüller Nils,
Grüne Lars
Publication year - 2012
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201210010
Subject(s) - controllability , model predictive control , heat equation , control theory (sociology) , boundary (topology) , stability (learning theory) , horizon , mathematics , exponential stability , exponential function , scheme (mathematics) , boundary value problem , mathematical optimization , control (management) , computer science , mathematical analysis , physics , nonlinear system , geometry , quantum mechanics , artificial intelligence , machine learning
We consider a model predictive control (MPC) scheme without stabilizing terminal constraints applied to the linear heat equation. We apply a method to analyze minimal stabilizing optimization horizons based on an exponential controllability condition. While the method is known to yield conservative quantitative results for concrete examples, our analysis shows that it precisely determines qualitative changes in the horizon for changing parameters and changing problem structures. Particularly, it is able to explain numerically observed differences in the stability behavior of MPC for distributed and for boundary control (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)