Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China.
Neural Netw. 2023 Sep;166:595-608. doi: 10.1016/j.neunet.2023.07.041. Epub 2023 Aug 3.
In this paper, N-cluster games with coupling and private constraints are studied, where each player's cost function is nonsmooth and depends on the actions of all players. In order to seek the generalized Nash equilibrium (GNE) of the nonsmooth N-cluster games, a distributed seeking neurodynamic approach with two-time-scale structure is proposed. An adaptive leader-following consensus technique is adapted to dynamically adjust parameters according to the degree of consensus violation, so as to quickly obtain accurate estimation information of other players' actions which facilitates the evaluation of its own cost. Benefitting from the unique structure of the approach based on primal dual and adaptive penalty methods, the players' actions enter the constraints while completing the seeking for GNE. As a result, the neurodynamic approach is completely distributed, and prior estimation of penalty parameters is avoided. Finally, two engineering examples of power system game and company capacity allocation verify the effectiveness and feasibility of the neurodynamic approach.
本文研究了具有耦合和私有约束的 N 集群博弈，其中每个玩家的成本函数是非光滑的，并且依赖于所有玩家的行动。为了寻求非光滑 N 集群博弈的广义纳什均衡 (GNE)，提出了一种具有双时间尺度结构的分布式寻优神经动力学方法。采用自适应领导跟随一致性技术根据一致性违反程度动态调整参数，以便快速获得其他玩家行动的准确估计信息，从而有助于评估自身成本。受益于基于原始对偶和自适应惩罚方法的方法的独特结构，玩家的行动在完成对 GNE 的寻找时进入约束。因此，神经动力学方法是完全分布式的，避免了对惩罚参数的预先估计。最后，电力系统博弈和公司容量分配的两个工程实例验证了神经动力学方法的有效性和可行性。
