Constrained Aggregative Games with Second-Order Nonlinear Multi-Agent Systems on a Weight-Unbalanced Digraph

The paper investigates a constrained aggregative game problem with second-order nonlinear players, where the communication topology is a weight-unbalanced digraph. Firstly, a generalized Nash equilibrium (GNE) seeking algorithm based on the interior penalty function method is proposed to solve the aggregative game with inequality constraints, and ensuring that the constraints are always satisfied. A variable is also introduced to eliminate the imbalance caused by the weight-unbalanced communication network. Then, the stability of the proposed algorithm is proved by using Lyapunov theory. Finally, the effectiveness of the algorithm is verified by simulation.