Recursive Computation of Static Output Feedback Stochastic Nash Games for Weakly-Coupled Large-Scale Systems


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.10   pp.3022-3029
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.3022
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
stochastic Nash games,  state-dependent noise,  static output feedback,  recursive algorithm,  

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This paper discusses the infinite horizon static output feedback stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems. In order to construct the strategy, the conditions for the existence of equilibria have been derived from the solutions of the sets of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing the asymptotic structure along with the positive semidefiniteness for the solutions of CSAREs, recursive algorithm for solving CSAREs is derived. As a result, it is shown that the proposed algorithm attains the reduced-order computations and the reduction of the CPU time. As another important contribution, the uniqueness of the strategy set is proved for the sufficiently small parameter ε. Finally, in order to demonstrate the efficiency of the proposed algorithm, numerical example is given.