We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on consensus and primal–dual gradient dynamics, to seek a generalized Nash equilibrium in networks of single-integrator agents. Our first solution adopts a fixed gain, whose choice requires the knowledge of some global parameters of the game. To relax this requirement, we conceive a controller that can be tuned in a completely decentralized fashion, thanks to the use of uncoordinated integral adaptive weights. We further introduce algorithms specifically devised for generalized aggregative games. Finally, we adapt all our control schemes to deal with heterogeneous multi-integrator agents and, in turn, with nonlinear feedback-linearizable dynamical systems. For all the proposed dynamics, we show convergence to a variational equilibrium, by leveraging monotonicity properties and stability theory for projected dynamical systems.

我们考虑在部分决策信息场景中具有凸可分离耦合约束的强单调博弈，该博弈由动态代理播放。我们从设计基于共识和原始-对偶梯度动力学的连续时间全分布反馈控制器开始，以寻求单集成代理网络中的广义Nash平衡。我们的第一个解决方案采用固定增益，其选择需要了解游戏的某些全局参数。为了放宽这一要求，我们设想了一种控制器，由于使用了不协调的积分自适应权重，因此可以完全分散地进行调节。我们进一步介绍专门为广义集合游戏设计的算法。最后，我们调整所有控制方案以应对异构的多集成商代理，然后，具有非线性反馈-可线性化的动力系统。对于所有拟议的动力学，我们通过利用单调性质和投影动力学系统的稳定性理论，证明收敛到变分平衡。