Continuous-Time Distributed Nash Equilibrium Seeking for Heterogeneous High-Order Systems in Aggregative Games Over Digraphs

This article investigates distributed Nash equilibrium (NE) seeking problem for aggregative games with heterogeneous higher-order integrator dynamics over weight-unbalanced digraphs. Each player possesses a local objective function that possesses not only its own strategy but also an aggregative term. First, by incorporating the compensator technique, an estimator with a consensus protocol is designed to distributed estimate this aggregative term. Second, a continuous-time distributed NE seeking algorithm is proposed by designing a state-feedback based controller, ensuring exponential convergence to NE. Moreover, the algorithm is analysed as exponentially stable through Lyapunov stability theory. Finally, the effectiveness of the algorithm is verified by numerical simulation.