Robust Incentive Stackelberg Games With a Large Population for Stochastic Mean-Field Systems
Robust Incentive Stackelberg Games With a Large Population for Stochastic Mean-Field Systems
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DOI：
10.1109/lcsys.2021.3135754
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发表时间：
2022
影响因子：
3
通讯作者：
H. Mukaidani;Shunpei Irie;Hua Xu;W. Zhuang
中科院分区：
文献类型：
--
作者：
H. Mukaidani;Shunpei Irie;Hua Xu;W. Zhuang
研究了平均场随机系统中具有大量群体的稳健激励 Stackelberg 博弈的静态输出反馈 (SOF) 策略。首先，基于随机代数矩阵方程（SAME）推导了外部扰动的鞍点平衡条件和控制策略。然后，通过重构追随者的激励策略和领导者的激励策略，导出中心化的SOF激励Stackelberg策略。此外，为了避免设计过程的高维性，提出了一种新的低维近似SOF激励Stackelberg策略的设计算法。结果表明，使用集中式 SOF 激励 Stackelberg 策略与使用低维近似 SOF 激励 Stackelberg 策略之间的均衡值差异为 $O(\sqrt {\varepsilon })=O(1/\sqrt {N})$ ，其中 $N$ 表示种群规模。最后，一个人口规模较大的数值例子证明了所提出的近似 SOF 激励 Stackelberg 策略的有效性。
A static output feedback (SOF) strategy for robust incentive Stackelberg games with a large population for mean-field stochastic systems is investigated. First, the saddle point equilibrium condition of external disturbance and control strategy is derived based on stochastic algebraic matrix equations (SAMEs). Then, a centralized SOF incentive Stackelberg strategy is derived through restructuring the follower’s strategies and the leader’s incentive strategy. Moreover, to avoid the high dimension of design procedure, a new designing algorithm of low-dimensional approximation SOF incentive Stackelberg strategy is proposed. It is shown that the difference in the equilibrium values between using the centralized SOF incentive Stackelberg strategy and using the low-dimensional approximation SOF incentive Stackelberg strategy is $O(\sqrt {\varepsilon })=O(1/\sqrt {N})$ , where $N$ denotes the population size. Finally, a numerical example with a large population size demonstrates the effectiveness of the proposed approximation SOF incentive Stackelberg strategy.