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Nonlinear Model Predictive Control

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Explicit Nonlinear Model Predictive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 429))

Abstract

A nonlinear model predictive control (NMPC) strategy requires the formulation of an optimization problem. For online NMPC the nonlinear programming problem must be solved numerically at every sampling interval, while explicit NMPC assumes that an explicit representation of the solution can be computed using multi-parametric nonlinear programming. This chapter considers the formulation of the optimization problem, which is an essential part of the control design and involves numerous decisions that are important for the control performance, stability, and robustness as well as the computational complexity and the numerical challenges of computing the solution. Key elements are discretization and parameterization procedures that leads to a finite-dimensional numerical optimal control problem that can be addressed using e.g. direct single shooting, direct multiple shooting, or collocation methods. Fundamental properties like feasibility and continuity of solutions are discussed, before various modifications that are needed to explicitly guarantee stability, feasibility, and robustness, are discussed. We then discuss further extensions for handling integer variables, output feedback, decentralized and distributed implementations, before some remarks on numerical and computational challenges are discussed at the end.

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Authors and Affiliations

  1. Institute of System Engineering and Robotics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Bl. 2, 1113, Sofia, Bulgaria

    Alexandra Grancharova

  2. Department of Engineering Cybernetics, Norwegian University of Science and Technology, O.S. Bragstads plass 2D, 7491, Trondheim, Norway

    Tor Arne Johansen

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  1. Alexandra Grancharova
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  2. Tor Arne Johansen
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Correspondence to Alexandra Grancharova .

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© 2012 Springer-Verlag GmbH Berlin Heidelberg

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Grancharova, A., Johansen, T.A. (2012). Nonlinear Model Predictive Control. In: Explicit Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28780-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-28780-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28779-4

  • Online ISBN: 978-3-642-28780-0

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