Distributed NE and GNE seeking for heterogeneous multi-player games over directed communication networks.

The non-cooperation game with heterogeneous dynamics is of both theoretical significance and practical relevance because of its extensive penetration into various fields, such as the game confrontation composed of unmanned aerial vehicles and unmanned vehicles or the power generation systems with varied turbine assemblies. To solve such a game problem, this paper investigates distributed Nash equilibrium (NE) and generalized Nash equilibrium (GNE) seeking problems for heterogeneous multi-player systems in non-cooperation games. First, by incorporating the output regulation technique, a distributed NE seeking strategy is designed for heterogeneous multi-player games over undirected communication networks. Then, the GNE seeking problem subject to coupling constraints among multiple players is further studied and a distributed GNE seeking strategy is developed by utilizing the Lagrange multiplier and the output regulation technique. Second, in the case of directed communication networks, both distributed NE and GNE seeking strategies are proposed by employing new type of auxiliary variables to compensate for the unbalanced networks. Compared with some existing results on distributed NE and GNE seeking strategies, both the dynamics of players and communication networks are extended further. Finally, numerical simulations are presented to show the effectiveness of the NE and GNE seeking strategies.