Soft-constrained stochastic Nash games for weakly coupled large-scale systems
Soft-constrained stochastic Nash games for weakly coupled large-scale systems
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DOI：
10.1016/j.automatica.2008.12.020
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发表时间：
2009-05
期刊：
影响因子：
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通讯作者：
H. Mukaidani
中科院分区：
文献类型：
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作者：
H. Mukaidani
本文讨论了弱耦合大系统中包含状态相关噪声的无限视界软约束随机纳什对策。首先，我们制定线性二次微分对策，其中鲁棒性达到对模型不确定性。值得注意的是，这是第一次基于交叉耦合随机代数Riccati方程（CSAREs）的解推导出鲁棒平衡点存在的条件。在建立了CSAREs解的一个具有正确定性的渐近结构后，利用牛顿法导出了一种求解CSAREs解的递归算法。作为另一个重要特征，我们提出了一种基于迭代解的高阶近似纳什策略。最后，通过一个算例验证了所提算法的有效性。
In this paper, we discuss infinite-horizon soft-constrained stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems. First, we formulate linear quadratic differential games in which robustness is attained against model uncertainty. It is noteworthy that this is the first time conditions for the existence of robust equilibria have been derived based on the solutions of sets of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing an asymptotic structure with positive definiteness for CSAREs solutions, we derive a recursive algorithm by means of Newton’s method so that it can be used to obtain solutions for CSAREs. As another important feature, we propose a high-order approximate Nash strategy based on iterative solutions. Finally, we provide a numerical example to verify the efficiency of the proposed algorithms.