Byzantine Agents’ Detection in Distributed Nash Equilibrium Seeking Algorithms Using an Adaptive Event-Triggered Scheme

In this article, a resilient, adaptive event-triggered distributed Nash equilibrium seeking algorithm is investigated for a class of multimicrogrid systems. Since the strategy of each microgrid affects others’ costs through total generation cost, such interaction among microgrids is modeled as a noncooperative game. To reduce unnecessary signal transmission among the aggregators, an adaptive algorithm, where threshold parameters are adjusted based on the behavior of the estimated signals in the last two iterations, is proposed. It is observed that when false data is injected into an agent, its estimated signals begin to diverge from the equilibrium point, and as a result, the threshold value becomes increasing. Furthermore, the misbehaving agents are identified and isolated using a reputation-based mechanism and are allowed to rejoin the network when they behave normally again. To deal with arbitrary behavior of users, receding horizon scheme of predictive control is used. Finally, a set of simulation results is presented to evaluate the effectiveness of the suggested algorithm.