Recursive Computation of Static Output Feedback Stochastic Nash Games for Weakly-Coupled Large-Scale Systems
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.3022-3029
- Publication Date
- 2008/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.10.3022
- Type of Manuscript
- PAPER
- Category
- Systems and Control
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Muneomi SAGARA, Hiroaki MUKAIDANI, Toru YAMAMOTO, "Recursive Computation of Static Output Feedback Stochastic Nash Games for Weakly-Coupled Large-Scale Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 10, pp. 3022-3029, October 2008, doi: 10.1093/ietfec/e91-a.10.3022.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.10.3022/_p
Copy
@ARTICLE{e91-a_10_3022,
author={Muneomi SAGARA, Hiroaki MUKAIDANI, Toru YAMAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Recursive Computation of Static Output Feedback Stochastic Nash Games for Weakly-Coupled Large-Scale Systems},
year={2008},
volume={E91-A},
number={10},
pages={3022-3029},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e91-a.10.3022},
ISSN={1745-1337},
month={October},}
Copy
TY - JOUR
TI - Recursive Computation of Static Output Feedback Stochastic Nash Games for Weakly-Coupled Large-Scale Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3022
EP - 3029
AU - Muneomi SAGARA
AU - Hiroaki MUKAIDANI
AU - Toru YAMAMOTO
PY - 2008
DO - 10.1093/ietfec/e91-a.10.3022
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2008
AB - 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.
ER -
English
