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Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

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  • I. Ivanov
  • Lars Imsland
  • B. Bogdanova

Abstract

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Suggested Citation

  • I. Ivanov & Lars Imsland & B. Bogdanova, 2017. "Iterative algorithms for computing the feedback Nash equilibrium point for positive systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 729-737, March.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:4:p:729-737
    DOI: 10.1080/00207721.2016.1212431
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    References listed on IDEAS

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    1. W. A. van den Broek & J. C. Engwerda & J. M. Schumacher, 2003. "Robust Equilibria in Indefinite Linear-Quadratic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 565-595, December.
    2. Youmei Zhang & Qingling Zhang & Tamaki Tanaka & Min Cai, 2013. "Admissibility for positive continuous-time descriptor systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(11), pages 2158-2165.
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