Distributed Algorithm Design for Aggregative Games of Euler–Lagrange Systems and Its Application to Smart Grids

The aggregative games are addressed in this article, in which there are coupling constraints among decisions and the players have Euler-Lagrange (EL) dynamics. On the strength of gradient descent, state feedback, and dynamic average consensus, two distributed algorithms are developed to seek the variational generalized Nash equilibrium (GNE) of the game. This article analyzes the convergence of two algorithms by utilizing singular perturbation analysis and variational analysis. The two algorithms exponentially and asymptotically converge to the variational GNE of the game, respectively. Moreover, the results are applied to the electricity market games of smart grids. By the algorithms, turbine-generator systems can seek the variational GNE of electricity markets autonomously. Finally, simulation examples verify the methods.