ISSN : 1796-203X
Volume : 3    Issue : 9    Date : September 2008

Efficient Numerical Computations of Soft Constrained Nash Strategy for Weakly Coupled Large-
Scale Systems
Muneomi Sagara, Hiroaki Mukaidani, and Toru Yamamoto
Page(s): 2-10
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In this paper, a high-order soft constrained Nash strategy for weakly coupled large-scale systems is
investigated. In order to solve the cross-coupled sign-indefinite algebraic Riccati equations
(CSAREs) corresponding to strategy, the iterative algorithm on the basis of the Newton’s method is
first applied. Second, the recursive algorithm for solving the CSAREs is also established to reduce  
the amount of algebraic computation as compared with the Newton’s method. Using these iterative
solutions, a highorder soft-constrained Nash strategy is designed. As a result, it is proved that the
proposed high-order approximate equilibrium strategies achieve better performance. Finally, in
order to demonstrate the efficiency of the algorithm, a numerical example is given.

Index Terms
soft constrained Nash strategy, weakly coupled large-scale systems, cross-coupled sign-indefinite
algebraic Riccati equations (CSAREs), Newton’s method, recursive algorithm, high-order
approximate equilibrium strategies