Numerical solution of stochastic Nash games with state-dependent noise for weakly coupled large-scale systems

Sagara Muneomi

Mukaidani Hiroaki

Yamamoto Toru

Applied Mathematics and Computation

This paper discusses the infinite horizon stochastic Nash games with state-dependent noise. After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross-coupled stochastic algebraic Riccati equations (CSAREs), a new algorithm that combines Newton's method with two fixed point algorithms for solving the CSAREs is derived. As a result, it is shown that the proposed algorithm attains quadratic convergence and the reduced-order computations for sufficiently small parameter ε. As another important feature, the high-order approximate strategy that is based on the iterative solutions is proposed. Using such strategy, the degradation of the cost functional is investigated. Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided.

stochastic Nash games

cross-coupled stochastic algebraic Riccati equations

CSAREs

Newton's method

Newton–Kantorovich theorem

fixed point algorithm

Mechanical engineering [ 530 ]

eng

Elsevier Inc

Copyright (c) 2007 Elsevier Inc

[ISSN] 0096-3003

[DOI] 10.1016/j.amc.2007.08.019

[NCID] AA00543329

[DOI] http://dx.doi.org/10.1016/j.amc.2007.08.019 isVersionOf