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.