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Real-Time Implementation of Explicit Model Predictive Control

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Handbook of Model Predictive Control

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

Abstract

This chapter explains the synthesis of explicit MPC feedback laws that allow for real-time implementation on hardware with limited computational and storage properties. Four methods are introduced. The first one replaces the potentially complex explicit MPC controller by a simpler feedback law by exploiting the geometry of explicit solutions. The second method reduces the storage footprint of explicit MPC by a complete elimination of critical regions, replaced by a direct evaluation of optimality conditions. The common denominator of both methods is that they preserve optimality while considerably reducing the complexity. The third method trades lower complexity for suboptimality while simultaneously minimizing the performance loss. Finally, a method for designing stabilizing explicit MPC controllers for control of nonlinear systems is introduced.

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Notes

  1. 1.

    If \(G_{\mathcal{A}}\) does not have a full row rank, it is always possible to identify a subset of \(\mathcal{A}\) such that all rows of \(G_{\mathcal{A}}\) are linearly independent, see, e.g., [37].

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Acknowledgements

M. Kvasnica, J. Holaza, and P. Bakarac gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 15-0007.

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Authors and Affiliations

  1. Slovak University of Technology in Bratislava, Bratislava, Slovakia

    Michal Kvasnica, Juraj Holaza & Peter Bakaráč

  2. EPFL Lausanne, Lausanne, Switzerland

    Colin N. Jones, Ivan Pejcic & Milan Korda

Authors
  1. Michal Kvasnica
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  2. Colin N. Jones
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  3. Ivan Pejcic
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  4. Juraj Holaza
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  5. Milan Korda
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  6. Peter Bakaráč
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Corresponding author

Correspondence to Michal Kvasnica .

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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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Kvasnica, M., Jones, C.N., Pejcic, I., Holaza, J., Korda, M., Bakaráč, P. (2019). Real-Time Implementation of Explicit Model Predictive Control. 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_17

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  • DOI: https://doi.org/10.1007/978-3-319-77489-3_17

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  • Publisher Name: Birkhäuser, Cham

  • Print ISBN: 978-3-319-77488-6

  • Online ISBN: 978-3-319-77489-3

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