JOURNAL OF COMPUTERS (JCP)

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

Full Text: PDF (379 KB)

**Abstract**

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

ISSN : 1796-203X

Volume : 3 Issue : 9 Date : September 2008

Page(s): 2-10

Full Text: PDF (379 KB)

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.

algebraic Riccati equations (CSAREs), Newton’s method, recursive algorithm, high-order

approximate equilibrium strategies