Robust SOF Stackelberg game for stochastic LPV systems
Robust SOF Stackelberg game for stochastic LPV systems
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DOI：
10.1007/s11432-021-3302-5
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
H. Mukaidani;Hua Xu
中科院分区：
文献类型：
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作者：
H. Mukaidani;Hua Xu
研究了随机线性参数变化(LPV)系统中具有多跟随者的鲁棒静态输出反馈Stackelberg对策。利用交叉耦合矩阵不等式建立了∞约束下的鲁棒SOF-Stackelberg策略的存在条件。为了确定该策略集，定义了与相关费用界相对应的优化问题，并利用Karush-Kuhn-Tucker条件导出了它们的解集。结果表明，通过求解高阶交叉耦合矩阵方程(CCME)可以得到稳健的SOF-Stackelberg策略集。针对CCME复杂且难以数值求解的特点，将CCME与CCMI相结合，提出了一种启发式算法。利用KM迭代算法证明了算法的收敛性质。最后，通过两个算例验证了该启发式算法的可靠性和有效性。
A robust static output feedback (SOF) Stackelberg game with multiple followers in stochastic linear parameter varying (LPV) systems is investigated. The conditions for the existence of a robust SOF Stackelberg strategy set underH∞constraints are established by the cross-coupled matrix inequality (CCMI). To determine this strategy set, the optimization problems corresponding to the relevant cost bounds are defined, and their solution sets are derived using the Karush-Kuhn-Tucker conditions. The results show that the robust SOF Stackelberg strategy set can be obtained by solving higher-order cross-coupled matrix equations (CCMEs). Because CCMEs are complex and difficult to solve numerically, a heuristic algorithm is developed by combining the CCMEs with the CCMIs. The convergence property is proven using the Krasnoselskii-Mann (KM) iteration algorithm. Finally, two numerical examples are solved to demonstrate the reliability and usefulness of the proposed heuristic algorithm.