A numerical analysis of the Nash strategy for weakly coupled large-scale systems
A numerical analysis of the Nash strategy for weakly coupled large-scale systems
复制标题
DOI：
10.1109/tac.2006.878744
复制
发表时间：
2006-08
影响因子：
6.8
通讯作者：
H. Mukaidani
中科院分区：
文献类型：
--
作者：
H. Mukaidani
本文讨论了无限视界大规模互联系统线性二次n人纳什对策的反馈纳什均衡。利用牛顿-坎托洛维奇定理，建立了交叉耦合代数Riccati方程的渐近结构及其解的唯一性和正半恒性。本研究的主要贡献是提出了一种求解CAREs的新算法。为了提高算法的收敛速度，将牛顿法与一种新的解耦算法相结合；结果表明，该算法具有二次收敛性。此外，还首次证明了用降阶计算方法求解独立代数Lyapunov方程（ALE）可以得到这些方程的解
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