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International Conference on Informatics in Control, Automation and Robotics

ICINCO 2018: Informatics in Control, Automation and Robotics pp 118–141Cite as

Automated Nonlinear Control Structure Design by Domain of Attraction Maximization with Eigenvalue and Frequency Domain Specifications

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 613))

Abstract

This work proposes a new method for nonlinear control structure design for nonlinear dynamical systems by grammatical evolution. The optimization is based on a novel fitness function which implements three different design objectives. First, the closed loop eigenvalues of the linearized system dynamics are restricted to be located in a predefined region of the complex plane. Second, design specifications on the frequency magnitude of the sensitivity transfer functions of the linearized system dynamics are imposed. Third, the estimated domain of attraction of the nonlinear closed loop system dynamics is maximized by evaluating a quadratic Lyapunov function, obtained by the solution of the Lyapunov equation, with a Monte-Carlo sampling algorithm. Additionally, a general formula for the centroid of a design region for pole placement is derived analytically and embedded in the optimization framework. The generated controllers are evaluated on a common, nonlinear benchmark system. It is shown that the proposed method can efficiently generate control laws which meet the imposed design specifications on the closed loop system while maximizing the domain of attraction.

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Author information

Authors and Affiliations

  1. BMW Group, Knorrstr. 147, 80788, Munich, Germany

    Elias Reichensdörfer

  2. BMW M GmbH, Daimlerstr. 19, 85748, Garching near Munich, Germany

    Dirk Odenthal

  3. Chair of Automatic Control Engineering, Technical University of Munich, Theresienstr. 90, 80333, Munich, Germany

    Elias Reichensdörfer & Dirk Wollherr

Authors
  1. Elias Reichensdörfer
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  2. Dirk Odenthal
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  3. Dirk Wollherr
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Corresponding author

Correspondence to Elias Reichensdörfer .

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Editors and Affiliations

  1. Ford Research and Advanced Engineer, Dearborn, MI, USA

    Oleg Gusikhin

  2. University of Paris-EST Créteil (UPEC), Créteil, France

    Kurosh Madani

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Reichensdörfer, E., Odenthal, D., Wollherr, D. (2020). Automated Nonlinear Control Structure Design by Domain of Attraction Maximization with Eigenvalue and Frequency Domain Specifications. In: Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics. ICINCO 2018. Lecture Notes in Electrical Engineering, vol 613. Springer, Cham. https://doi.org/10.1007/978-3-030-31993-9_6

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