广东工业大学学报 ›› 2024, Vol. 41 ›› Issue (02): 129-138.doi: 10.12052/gdutxb.230010
• 综合研究 • 上一篇
张成科1, 徐萌2, 杨璐3
Zhang Cheng-ke1, Xu Meng2, Yang Lu3
摘要: 考虑到转移概率矩阵元素无法完全获悉,如何在转移概率部分未知的情境下研究离散时间Markov跳变系统Nash微分博弈是有待解决的问题之一,这一问题可以为转移概率部分未知的Markov跳变系统Nash微分博弈理论在管理问题上的应用提供理论支撑。基于此,本文首先研究单人博弈情形,即ε-次优控制问题,借助自由连接权矩阵和配方法,得到了ε-次优控制策略存在的充分性条件,并给出了成本函数上界的显式表达;然后延伸至双人博弈进行分析,得到了ε-次优Nash均衡策略存在的条件等价于求解双线性矩阵不等式和矩阵不等式的优化问题,并通过启发式算法求解优化问题得到ε-次优Nash均衡策略;最后通过数值算例证明了主要结论的有效性。
中图分类号:
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