Distributed Aggregative Game for Multi-Agent Systems With Heterogeneous Integrator Dynamics

Distributed aggregative games have been intensely researched due to their wide application in various engineering scenarios. This brief aims to address the distributed aggregative game over the multi-agent system with heterogeneous high-order integrator dynamics and undirected, connected networks. In this game, the local objective function incorporates its local decision variable and an aggregative term that combines all agents' decision variables. The aggregative term is estimated using the consensus method. Therefore, the Nash equilibrium-seeking strategy is created using the gradient descent flow and state feedback control technologies. In addition, it is proved that the Nash equilibrium is achieved with an exponential convergence rate through the use of the Lyapunov theory. Finally, the strategy's utility is evaluated by two simulation examples.