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

IEEE Transactions on Automatic Control 51 巻 8 号 1371-1377 頁 2006-08 発行
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タイトル ( eng )
A numerical analysis of the Nash strategy for weakly coupled large-scale systems
作成者
収録物名
IEEE Transactions on Automatic Control
51
8
開始ページ 1371
終了ページ 1377
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.
著者キーワード
Cross-coupled algebraic Riccati equations (CARE)
Fixed-point algorithm
Nash games
Newton's method
Weakly coupled large-scale systems
NDC分類
数学 [ 410 ]
言語
英語
資源タイプ 学術雑誌論文
出版者
IEEE
発行日 2006-08
権利情報
Copyright (c) 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
出版タイプ Version of Record(出版社版。早期公開を含む)
アクセス権 オープンアクセス
収録物識別子
[ISSN] 0018-9286
[DOI] 10.1109/TAC.2006.878744
[NCID] AA00667671
[DOI] http://dx.doi.org/10.1109/TAC.2006.878744