Fully Distributed Game Strategy for Second-Order Players and Its Application to Networked Electricity Markets

In this paper, we study the noncooperative games (NGs) of multi-agent systems. In our problem, the players have private payoff functions, and their decisions are subject to local and coupling nonlinear inequality constraints. Moreover, our problem contains second-order dynamical systems of players. To control these second-order players to autonomously participate in the games, a distributed adaptive strategy is proposed based on state feedback and primal-dual methods. With our method, the updates of the control inputs of all players depend only on their own and neighbors' information, and are independent of global parameters or variables, different from other related methods. By virtue of variational analysis and LaSalle invariance principle, it is proved that our strategy converges to the variational Generalized Nash Equilibrium (v-GNE) of the games. Finally, the proposed method is applied to networked electricity market games of smart grids.