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Numerical Algorithm for Solving Cross-Coupled Algebraic Riccati Equations of Singularly Perturbed Systems

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 7))

Abstract

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems (SPS). In order to solve the generalized algebraic Lyapunov equation (GALE) corresponding to the generalized Lyapunov iterations, we propose a new algorithm which is based on the fixed point iterations. Furthermore, we also propose a new algorithm which is based on the Kleinman algorithm for solving the generalized cross-coupled algebraic Riccati equations (GCARE). It is shown that the resulting algorithm guarantees the quadratic convergence.

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Author information

Authors and Affiliations

  1. Graduate School of Education, Hiroshima University, Japan

    Hiroaki Mukaidani

  2. Graduate School of Business Sciences, The University of Tsukuba, Japan

    Hua Xu

  3. Graduate School of Engineering, Hiroshima Kokusai Gakuin University, Japan

    Koichi Mizukami

Authors
  1. Hiroaki Mukaidani
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  2. Hua Xu
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  3. Koichi Mizukami
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wypiańskiego 27, 50-370, Wrocław, Poland

    Andrzej S. Nowak  & Krzysztof Szajowski  & 

  2. Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland

    Andrzej S. Nowak

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© 2005 Birkhäuser Boston

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Mukaidani, H., Xu, H., Mizukami, K. (2005). Numerical Algorithm for Solving Cross-Coupled Algebraic Riccati Equations of Singularly Perturbed Systems. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_29

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