Event-Triggered Adaptive Nash Equilibrium Seeking Algorithm Over Unbalanced Digraph

The noncooperative game with private constraints is studied, where heterogeneous players communicate over a weight-unbalanced digraph. A novel distributed Nash equilibrium (NE) seeking algorithm is adapted for this problem tackling two main difficulties. First, the presence of the unbalanced digraph disrupts some essential properties of the Laplacian matrix. To overcome this limitation, a compensation mechanism based on output feedback is introduced. Second, to ensure players' actions meet the constraints, an adaptive penalty technique is introduced. This technique effectively uses the information obtained from the intrinsic nature of the constraints and fulfills the quantitative estimation of penalty parameters, where the penalty parameters are able to vary along with the degree of constraint violation. To reduce unnecessary communication among players, a novel distributed NE seeking algorithm with a bivariate dynamic event-triggered mechanism is employed, which ensures exponential NE seeking while avoiding the Zeno behavior. Finally, a connectivity control game is given to evaluate the effectiveness of the results.