A Numerical Analysis of the Nash Strategy for Weakly Coupled Large-Scale Systems

Hiroaki Mukaidani

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A Numerical Analysis of the Nash Strategy for Weakly Coupled Large-Scale Systems

机译：弱耦合大型系统纳什策略的数值分析

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This 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.

机译：本文讨论了无限水平大型互联系统的线性二次N玩家Nash游戏的反馈Nash平衡。通过牛顿-坎托罗维奇定理，建立了交叉耦合代数Riccati方程（CAREs）解的唯一性和正半定性。这项研究的主要贡献是提出了一种解决CARE的新算法。为了提高算法的收敛速度，牛顿法与一种新的解耦算法相结合。结果表明，所提算法具有二次收敛性。此外，这首次表明可以通过使用降阶计算来求解独立代数Lyapunov方程（ALE）来获得CARE的解。

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《IEEE Transactions on Automatic Control》 |2006年第8期|p.1371-1377|共7页
作者
Hiroaki Mukaidani;
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正文语种 eng
中图分类自动化系统;
关键词
Cross-coupled algebraic Riccati equations (CARE); Fixed-point algorithm; Nash games; Newton's method; Weakly coupled large-scale systems;

机译：交叉耦合代数Riccati方程（CARE）;定点算法;纳什博弈;牛顿法;弱耦合大型系统;

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A Numerical Analysis of the Nash Strategy for Weakly Coupled Large-Scale Systems

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