Collisions-Free Distributed Nash Equilibrium Seeking for Constrained Noncooperative Games of Second-order Systems

The the collision-free Nash equilibrium seeking problem is studied for the second order systems where the nonlinear coupled inequality constraints are considered for all players decisions in this paper. Moreover, the collision-free between players can be ensured by the control barrier function methods. The convergence of all the player is analyzed with the designed algorithm and the variational generalized Nash equilibrium of the games can be seek. Furthermore, based on the designed algorithm, by combining the control barrier function and control Lyapunov function via quadratic programs, collision-free is ensured in the process of seeking Nash equilibrium. Finally, a comparative example is proposed to verify the effectiveness of our algorithm.