Nash Games for Weakly-Coupled Large-Scale Markovian Jump Stochastic Systems

• Sagara Muneomi

  Facalty of Administration, Prefectural University of Kumamoto

• Mukaidani Hiroaki

  Graduate School of Education, Hiroshima University

Bibliographic Information

Other Title

• 弱結合大規模マルコフジャンプ確率システムのためのナッシュゲーム
• ジャク ケツゴウ ダイキボ マルコフジャンプ カクリツ システム ノ タメ ノ ナッシュゲーム

Abstract

In this paper, the stochastic Nash games for stochastic Markov jump systems are investigated. First, the Nash equilibrium is defined and the existence conditions are formulated. In particular, necessary and sufficient conditions for the existence of two cross-coupled stochastic algebraic Riccati equations (CSAREs) are developed. Moreover, in order to obtain the required solutions, a numerical algorithm that is based on the Newton's method is proposed. As an important implication, weakly-coupled large-scale systems are also adopted. After establishing the asymptotic structure of the solutions for the CSAREs, the quadratic convergence result that is based on the Newton's method is shown. Finally, a numerical example is given to demonstrate the availability of the proposed method.

Journal

• IEEJ Transactions on Electronics, Information and Systems

  IEEJ Transactions on Electronics, Information and Systems 131 (3), 644-654, 2011

  The Institute of Electrical Engineers of Japan

Keywords

• Weakly coupled large-scale stochastic systems
• Markov jump systems
• Nash games
• cross-coupled stochastic algebraic Riccati equation
• Numerical algorithm

Details

• CRID: 1390001204609210240
• NII Article ID: 10027804553
• NII Book ID: AN10065950
• DOI: 10.1541/ieejeiss.131.644
• ISSN: 13488155
• ISSN: 03854221
• NDL BIB ID: 10986387
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10986387
• Web Site: https://www.jstage.jst.go.jp/article/ieejeiss/131/3/131_3_644/_pdf
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed