论文标题
分布式NASH平衡寻求在具有未知控制方向的系统中寻找游戏
Distributed Nash Equilibrium Seeking for Games in Systems with Unknown Control Directions
论文作者
论文摘要
本文探讨了分布式的NASH平衡在不确定的网络系统中寻找游戏中的游戏，但在本文中探讨了有关控制方向的先验知识。更具体地说，玩家的动力学应该是一阶或二阶系统，其中控制方向未知并且存在参数不确定性。为了以分布式方式实现NASH平衡寻求，通过单独设计优化模块和状态调节模块，提出了基于Nussbaum函数的策略。优化模块生成一个参考轨迹，可以搜索状态调节模块的NASH平衡。州监管机构旨在将玩家的动作引导到参考轨迹上。州监管模块中包含了自适应定律，以补偿玩家动力学中的不确定参数，并包括Nussbaum功能以解决控制方向的不可用。讨论并研究了所提出算法的完全分布式实现。通过我们的分析探索，我们表明拟议的寻求策略可以渐近地推动玩家的行动对NASH均衡，而无需基于Barbalat的引理的玩家的均匀性。给出了一个数值示例，以支持所提出算法的理论分析。
Distributed Nash equilibrium seeking for games in uncertain networked systems without a prior knowledge about control directions is explored in this paper. More specifically, the dynamics of the players are supposed to be first-order or second-order systems in which the control directions are unknown and there are parametric uncertainties. To achieve Nash equilibrium seeking in a distributed way, Nussbaum function based strategies are proposed through separately designing an optimization module and a state regulation module. The optimization module generates a reference trajectory, that can search for the Nash equilibrium, for the state regulation module. The state regulator is designed to steer the players' actions to the reference trajectory. An adaptive law is included in the state regulation module to compensate for the uncertain parameter in the players' dynamics and the Nussbaum function is included to address the unavailability of the control directions. Fully distributed implementations of the proposed algorithms are discussed and investigated. Through our analytical explorations, we show that the proposed seeking strategies can drive the players' actions to the Nash equilibrium asymptotically without requiring the homogeneity of the players' unknown control directions based on Barbalat's lemma. A numerical example is given to support the theoretical analysis of the proposed algorithms.
