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Data-Driven Nonlinear Stabilization Using Koopman Operator

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The Koopman Operator in Systems and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 484))

Abstract

We propose the application of Koopman operator theory for the design of stabilizing feedback controller for a nonlinear control system. The proposed approach is data-driven and relies on the use of time-series data generated from the control dynamical system for the lifting of a nonlinear system in the Koopman eigenfunction coordinates. In particular, a finite-dimensional bilinear representation of a control-affine nonlinear dynamical system is constructed in the Koopman eigenfunction coordinates using time-series data. Sample complexity results are used to determine the data required to achieve the desired level of accuracy for the approximate bilinear representation of the nonlinear system in Koopman eigenfunction coordinates. A control Lyapunov function-based approach is proposed for the design of stabilizing feedback controller. A systematic convex optimization-based formulation is proposed for the search of control Lyapunov function. Several numerical examples are presented to demonstrate the application of the proposed data-driven stabilization approach.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Iowa State University, Ames, IA, 50011, USA

    Bowen Huang

  2. Pacific Northwest National Laboratory, Richland, WA, 99352, USA

    Xu Ma

  3. Department of Mechanical Engineering, Clemson University, Clemson, SC, 29634, USA

    Umesh Vaidya

Authors
  1. Bowen Huang
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  2. Xu Ma
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  3. Umesh Vaidya
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Corresponding author

Correspondence to Umesh Vaidya .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Namur, Namur, Belgium

    Alexandre Mauroy

  2. Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA, USA

    Igor Mezić

  3. Department of Electrical and Information Systems, Osaka Prefecture University, Sakai, Japan

    Yoshihiko Susuki

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Huang, B., Ma, X., Vaidya, U. (2020). Data-Driven Nonlinear Stabilization Using Koopman Operator. In: Mauroy, A., Mezić, I., Susuki, Y. (eds) The Koopman Operator in Systems and Control. Lecture Notes in Control and Information Sciences, vol 484. Springer, Cham. https://doi.org/10.1007/978-3-030-35713-9_12

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