Soft-constrained stochastic Nash games for weakly coupled large-scale discrete-time systems
Soft-constrained stochastic Nash games for weakly coupled large-scale discrete-time systems
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DOI：
10.1109/cdc.2011.6160359
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
H. Mukaidani;Hua Xu;V. Drăgan
中科院分区：
文献类型：
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作者：
H. Mukaidani;Hua Xu;V. Drăgan
本文讨论了弱耦合大尺度离散系统中包含状态相关噪声和确定性不确定性的无限视界软约束随机纳什对策。首先，我们建立了线性二次型软约束纳什对策，该对策对外部干扰具有鲁棒性。然后，根据离散型交叉耦合随机代数Riccati方程（CSAREs）的集合解，导出了鲁棒平衡存在的条件。此外，还分析了均方稳定性等各种可靠特性。在建立了CSAREs解的一个具有正确定性的渐近结构后，导出了求解CSAREs的递归算法。最后，通过一个算例验证了所提方法的有效性。
In this paper, we discuss infinite-horizon soft-constrained stochastic Nash games involving state-dependent noise and deterministic uncertainties in weakly coupled large-scale discrete-time systems. First, we formulate linear quadratic soft-constrained Nash games in which robustness is attained against external disturbance. Then, the conditions for the existence of robust equilibrium are derived based on the solutions of sets of the discrete version of cross-coupled stochastic algebraic Riccati equations (CSAREs). Moreover, various reliable features such as mean square stability are analyzed. After establishing an asymptotic structure along with positive definiteness for CSAREs solutions, we derive the recursive algorithm for solving CSAREs. Finally, we provide a numerical example to verify the efficiency of the proposed method.