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Vector Relative Degree and Funnel Control for Differential-Algebraic Systems

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Progress in Differential-Algebraic Equations II

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

We consider tracking control for multi-input multi-output differential-algebraic systems. First, the concept of vector relative degree is generalized for linear systems and we arrive at the novel concept of “truncated vector relative degree”, and we derive a new normal form. Thereafter, we consider a class of nonlinear functional differential-algebraic systems which comprises linear systems with truncated vector relative degree. For this class we introduce a feedback controller which achieves that, for a given sufficiently smooth reference signal, the tracking error evolves within a pre-specified performance funnel.

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Notes

  1. 1.

    In [21] a domain \(\mathcal {D}\subseteq {\mathbb {R}}_{\ge 0}\times {\mathbb {R}}\) is considered, but the generalization to the higher dimensional case is straightforward.

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Acknowledgement

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) via the grant BE 6263/1-1.

Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Paderborn, Paderborn, Germany

    Thomas Berger

  2. Department of Mathematics, National University of Civil Engineering, Hai Ba Trung, Hanoi, Vietnam

    Huy Hoàng Lê

  3. Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

    Timo Reis

Authors
  1. Thomas Berger
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  2. Huy Hoàng Lê
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  3. Timo Reis
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Corresponding author

Correspondence to Thomas Berger .

Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

    Timo Reis

  2. Max-Planck-Institut für Dynamik komplexer technischer Systeme, Magdeburg, Sachsen-Anhalt, Germany

    Sara Grundel

  3. Technische Universität Darmstadt, Darmstadt, Germany

    Sebastian Schöps

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Berger, T., Lê, H.H., Reis, T. (2020). Vector Relative Degree and Funnel Control for Differential-Algebraic Systems. In: Reis, T., Grundel, S., Schöps, S. (eds) Progress in Differential-Algebraic Equations II. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/978-3-030-53905-4_8

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