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Numerical Algorithm for Solving Cross-Coupled Multiparameter Algebraic Riccati Equations of Multimodeling Systems Related to Nash Games

In: ICM Millennium Lectures on Games

Author

Listed:
  • Hiroaki Mukaidani

    (Hiroshima City University, Faculty of Information Sciences)

  • Tetsu Shimomura

    (Hiroshima University, Graduate School of Education)

  • Hua Xu

    (The University of Tsukuba, Graduate School of Business Sciences)

Abstract

Summary We study linear quadratic Nash games for infinite horizon multiparameter singularly perturbed systems (MSPS). We propose a new algorithm which is based on the Kleinman algorithm for solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). It is shown that the resulting algorithm guarantees quadratic convergence. Simulation results show that the proposed algorithm succeeds in dramatically improving the convergence rate compared with previous results.

Suggested Citation

  • Hiroaki Mukaidani & Tetsu Shimomura & Hua Xu, 2003. "Numerical Algorithm for Solving Cross-Coupled Multiparameter Algebraic Riccati Equations of Multimodeling Systems Related to Nash Games," Springer Books, in: Leon A. Petrosyan & David W. K. Yeung (ed.), ICM Millennium Lectures on Games, pages 359-371, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-05219-8_23
    DOI: 10.1007/978-3-662-05219-8_23
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