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Nonlinear Predictive Control for Trajectory Tracking and Path Following: An Introduction and Perspective

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Handbook of Model Predictive Control

Part of the book series: Control Engineering ((CONTRENGIN))

Abstract

Control tasks in various applications are posed as setpoint-stabilization problems, where a constant reference has to be stabilized. For systems where changing references are given, formulations for tracking of a time-dependent trajectory or for following a geometric path are more suitable. In other cases, no clear reference is given, but only optimal economic behavior is desired. We outline how these control goals can be captured and embedded in a model predictive control design and provide theoretic formulations. We compare trajectory tracking and path following in a realistic robot simulation example to highlight that it is important for an engineer to choose the appropriate formulation of the control task at hand.

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Notes

  1. 1.

    We focus on continuous-time systems described by differential equations. Extensions towards distributed parameter systems or discrete-time systems are subject to future work, respectively, easily possible.

  2. 2.

    The class of considered input functions could be readily extended to measurable controls. Here, for the sake of simplicity, we focus on the more application relevant setting of piecewise constant control signals.

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Acknowledgements

J. Matschek and R. Findeisen acknowledge support by the German Federal Ministry of Education and Research within the Forschungscampus STIMULATE under grant number 13GW0095A. T. Faulwasser acknowledges support from the Baden-Württemberg Stiftung under the Elite Programme for Postdocs.

Author information

Authors and Affiliations

  1. Laboratory for Systems Theory and Automatic Control, Otto-von-Guericke University Magdeburg, Magdeburg, Germany

    Janine Matschek, Tobias Bäthge & Rolf Findeisen

  2. International Max Planck Research School for Advanced Methods in Process and Systems Engineering, Magdeburg, Germany

    Tobias Bäthge & Rolf Findeisen

  3. Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Timm Faulwasser

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  1. Janine Matschek
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  2. Tobias Bäthge
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  3. Timm Faulwasser
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  4. Rolf Findeisen
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Editors and Affiliations

  1. Independent Researcher, London, UK

    Saša V. Raković

  2. Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA

    William S. Levine

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Matschek, J., Bäthge, T., Faulwasser, T., Findeisen, R. (2019). Nonlinear Predictive Control for Trajectory Tracking and Path Following: An Introduction and Perspective. In: Raković, S., Levine, W. (eds) Handbook of Model Predictive Control. Control Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77489-3_8

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