Distributed Nash Equilibrium Seeking Of Aggregative Games For High-Order Systems

In this paper, the Nash equilibrium seeking (NES) problem of aggregative games is investigated for high-order multi-agents systems, where the cost function for each agent depends on its decision variable and the aggregate of all other decisions. To solve the problem, we employ the embedded technology to decouple the primal problem into two parts: decision planning and tracking. We first construct a single integrator system for the NES to generate the optimal reference decision trajectory, and then we propose the distributed algorithms to make the nonlinear Euler-Lagrange (EL) systems and the general high-order linear system track the optimal reference decision path, respectively. Finally, simulations are given to validate the effectiveness of the theoretical analysis.