Convergence-guaranteed distributed Nash equilibrium seeking for second-order multi-agent systems in noncooperative formation games

This paper proposes a distributed Nash equilibrium seeking algorithm for second-order multi-agent formation games with directed communication topologies. The algorithm combines gradient-based optimization with a dynamic observer, enabling agents to reach Nash equilibrium while maintaining prescribed formations through local interactions. Using Lyapunov stability theory and singular perturbation analysis, we prove asymptotic convergence under strongly connected digraphs. Numerical simulations demonstrate the algorithm's effectiveness in achieving simultaneous equilibrium convergence and formation maintenance. The proposed method provides an effective solution for multi-robot formation control and autonomous swarm coordination.