This article investigates the distributed generalized Nash equilibrium (GNE) seeking problem of noncooperative games (NGs) for high-order strict-feedback nonlinear multiagent systems (MASs). In particular, the feasible action set of each agent is not only subject to local set and inequality constraints but also coupled through an equality constraint with other agents. This constraint structure is more general and covers most of the constraints in the GNE seeking literature. To accomplish the concerned GNE seeking objective, we propose a novel hierarchical GNE seeking approach in this article to decouple the distributed GNE seeking algorithm design into two layers. First, we construct a distributed primary-dual GNE estimator to generate virtual reference signals that converge to the GNE. Then, with the output of the estimator as the reference signal, we develop an adaptive tracking controller to solve the resultant tracking problems under output constraints. To overcome the negative effects of the disturbances, novel compensating terms associated with smooth functions and positive integrable time-varying functions are incorporated in the controller design, which thereby realizes the exact GNE seeking in the presence of nonvanishing mismatched disturbances. At last, an example is given to support the theoretical analysis of the proposed algorithms.

中文翻译：

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高阶不确定非线性系统的层次鲁棒广义纳什均衡求


本文研究了高阶严格反馈非线性多智能体系统 (MAS) 的非合作博弈 (NG) 的分布式广义纳什均衡 (GNE) 寻求问题。特别是，每个智能体的可行动作集不仅受到局部集和不等式约束，而且还通过等式约束与其他智能体耦合。这种约束结构更加通用，涵盖了 GNE 搜索文献中的大部分约束。为了实现相关的 GNE 搜索目标，我们在本文中提出了一种新颖的分层 GNE 搜索方法，将分布式 GNE 搜索算法设计解耦为两层。首先，我们构建一个分布式主对偶 GNE 估计器来生成收敛到 GNE 的虚拟参考信号。然后，以估计器的输出作为参考信号，我们开发了自适应跟踪控制器来解决输出约束下的跟踪问题。为了克服干扰的负面影响，控制器设计中纳入了与平滑函数和正可积时变函数相关的新颖补偿项，从而在存在非零失配干扰的情况下实现了精确的GNE搜索。最后，给出一个例子来支持所提出算法的理论分析。