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

Elias Reichensdörfer, Dirk Odenthal, Dirk Wollherr

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationInformatics in Control, Automation and Robotics - 15th International Conference, ICINCO 2018, Revised Selected Papers
EditorsOleg Gusikhin, Kurosh Madani
PublisherSpringer
Pages118-141
Number of pages24
ISBN (Print)9783030319922
DOIs
StatePublished - 2020
Event15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018 - Porto, Portugal
Duration: 29 Jul 201831 Jul 2018

Publication series

NameLecture Notes in Electrical Engineering
Volume613
ISSN (Print)1876-1100
ISSN (Electronic)1876-1119

Conference

Conference15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018
Country/TerritoryPortugal
CityPorto
Period29/07/1831/07/18

Keywords

  • Domain of attraction maximization
  • Frequency domain specifications
  • Grammatical evolution
  • Lyapunov equation
  • Nonlinear control structure design
  • Robust control
  • Stability centroid

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