An Adaptively Distributed Algorithm for Noncooperative Games of High-Order Integrator Systems

In this paper, an adaptively distributed Nash equilibrium (NE) seeking algorithm is designed for heterogeneous high-order integrators in noncooperative games. The adaptively distributed algorithm is proposed that introduces a scaling parameter with adaptive adjustments to the weights of the edges in the communication graph. The main advantage is to ensure the convergence of the algorithm to the NE without requiring the knowledge of graph's algebraic connectivity. The convergence of the designed algorithm to the NE is analyzed by the Lyapunov stability theory and input-to-state stability theory. A numerical example is given to illustrate the proposed method.