Abstract
This article investigates an aggregative game based on Euler-Lagrange systems subject to time-varying communication delays. First, a distributed algorithm is put forward to try to find the Nash equilibrium by the deliberated group of Euler-Lagrange systems with “small” delay and “large” delay. Second, we illustrate the convergence of two circumstances, separately. The first circumstance derives the upper bound of delays for guaranteeing globally exponential convergence, and the other obtains globally exponential convergence, even in some restrictions on “large” delays. Finally, a numerical example is used to show the effectiveness and superiority of proposed method.
Highlights
Aggregative games have been enormously received a great concern in many areas owing to their wide applications in areas of smart grid [1]–[3], plug-in electric vehicles [4]–[6], congestion control in communication networks with shared resources [7], [8]
The main contributions of this article can be concluded as follows: Firstly, we provide an aggregative game of Euler-Lagrange systems, which are subject to transmission delays
The first circumstance derives the upper bound of delays for guaranteeing globally exponential convergence, and the other obtains globally exponential convergence, even in some restrictions on ‘‘large’’ delays
Summary
Aggregative games have been enormously received a great concern in many areas owing to their wide applications in areas of smart grid [1]–[3], plug-in electric vehicles [4]–[6], congestion control in communication networks with shared resources [7], [8]. The main characteristics of the aggregative games is that the cost of each player depends on its own decision, and the average among the strategies of all other players. In response to such problems as aggregative games, extensive research has been exceedingly conducted on seeking Nash equilibrium to minimize their cost function Considering the aggregation games, the method of distributed design plays an increasingly significant role in the algorithm implementation, where players (agents) exchange data through local information and between neighbors via an undirected and connected communication graph. Ye and Hu [9] developed a leader-following consensus protocol, which can utilize the scheme of gradient play for
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