A numerical analysis of the Nash strategy for weakly coupled large-scale systems

• Mukaidani, Hiroaki

抄録

his note discusses the feedback Nash equilibrium of linear quadratic N-player Nash games for infinite-horizon large-scale interconnected systems. The asymptotic structure along with the uniqueness and positive semidefiniteness of the solutions of the cross-coupled algebraic Riccati equations (CAREs) is newly established via the Newton-Kantorovich theorem. The main contribution of this study is the proposal of a new algorithm for solving the CAREs. In order to improve the convergence rate of the algorithm, Newton's method is combined with a new decoupling algorithm; it is shown that the proposed algorithm attains quadratic convergence. Moreover, it is shown for the first time that solutions to the CAREs can be obtained by solving the independent algebraic Lyapunov equation (ALE) by using the reduced-order calculation.

収録刊行物

• IEEE Transactions on Automatic Control

  IEEE Transactions on Automatic Control 51 (8), 1371-1377, 2006-08

  IEEE

キーワード

• Cross-coupled algebraic Riccati equations (CARE)
• Fixed-point algorithm
• Nash games
• Newton's method
• Weakly coupled large-scale systems

詳細情報

• CRID: 1050577740964777600
• NII論文ID: 120000882389
• NII書誌ID: AA00667671
• DOI: 10.1109/tac.2006.878744
• ISSN: 00189286
• Web Site: http://ir.lib.hiroshima-u.ac.jp/00015012
• Web Site: http://xplorestaging.ieee.org/ielx5/9/35123/01673600.pdf?arnumber=1673600
• 本文言語コード: en
• 資料種別: journal article
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