In this paper, we propose distributed feedback control that steers a dynamical network to a prescribed equilibrium corresponding to the so-called Cournot–Nash equilibrium. The network dynamics considered here are a class of passive nonlinear second-order systems, where production and demands act as external inputs to the systems. While productions are assumed to be controllable at each node, the demand is determined as a function of local prices according to the utility of the consumers. Using reduced information on the demand, the proposed controller guarantees the convergence of the closed-loop system to the optimal equilibrium point dictated by the Cournot–Nash competition.

中文翻译：

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一种反馈控制算法，可将网络转向古诺-纳什均衡

在本文中，我们提出了分布式反馈控制，该控制将动态网络控制到与所谓的古诺-纳什均衡相对应的规定均衡。这里考虑的网络动力学是一类无源非线性二阶系统，其中生产和需求充当系统的外部输入。虽然假定每个节点的生产都是可控的，但根据消费者的效用，将需求确定为当地价格的函数。利用减少的需求信息，所提出的控制器可保证闭环系统收敛到古诺—纳什竞争所决定的最佳平衡点。