Distributed algorithms for aggregative games of multiple heterogeneous Euler-Lagrange systems

In this paper, an aggregative game of Euler-Lagrange (EL) systems is investigated, where the cost functions of all players depend on not only their own decisions but also the aggregate of all decisions. Two distributed algorithms are designed for these heterogeneous EL players to reach the Nash equilibrium of aggregative games. By constructing suitable Lyapunov functions, the convergence of the two algorithms are analyzed. The first algorithm achieves globally exponential convergence without parameter uncertainty, and the other achieves globally asymptotic convergence, even in the presence of uncertain parameters. Numerical examples are given to illustrate the effectiveness of the methods. (C) 2018 Elsevier Ltd. All rights reserved.