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

Mukaidani Hiroaki

IEEE Transactions on Automatic Control

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.

Cross-coupled algebraic Riccati equations (CARE)

Fixed-point algorithm

Nash games

Newton's method

Weakly coupled large-scale systems

Mathematics [ 410 ]

eng

IEEE

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[ISSN] 0018-9286

[DOI] 10.1109/TAC.2006.878744

[NCID] AA00667671

[DOI] http://dx.doi.org/10.1109/TAC.2006.878744