Event-triggered distributed Nash equilibrium seeking over directed graphs and its application to power management

Abstract

In this paper, the problem of distributed discrete-time Nash equilibrium computation with event-triggered communication over directed graphs is studied. Each agent can only receive strategies from its neighbors through a directed and unbalanced graph, while its cost function may rely on the information of all agents. To this end, each agent needs to estimate the strategy profile. Meanwhile, an event-triggered communication mechanism is introduced, which can effectively compensate for network resource loss. Concretely, specific moments that each agent transmits its information are decided by the pre-designed event-triggered condition. In this setting, two discrete-time Nash equilibrium seeking algorithms with event-triggered communication are designed, respectively considering that the Perron-Frobenius eigenvector of the adjacency matrix associated the directed communication graph is known and unknown in advance. It is rigorously proved that both algorithms can linearly converge to the Nash equilibrium with a small error. Finally, a power management example in smart grids is presented to verify the performance of proposed algorithms.