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A numerical analysis of the Nash strategy for weakly coupled large-scale systems Mukaidani, Hiroaki Mukaidani Hiroaki open access 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. Cross-coupled algebraic Riccati equations (CARE) Fixed-point algorithm Nash games Newton's method Weakly coupled large-scale systems 410 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. IEEE 2006-08 eng journal article VoR https://hiroshima.repo.nii.ac.jp/records/2007001 10.1109/TAC.2006.878744 http://dx.doi.org/10.1109/TAC.2006.878744 0018-9286 AA00667671 IEEE Transactions on Automatic Control IEEE Transactions on Automatic Control 51 8 1371 1371 1377 https://hiroshima.repo.nii.ac.jp/record/2007001/files/TN05-02-23.pdf 316.3 KB