$$\boldsymbol{\epsilon }$$-Nash Equilibrium Seeking for Two Order Multi-agent with Disturbance Rejection

In this paper, we investigate an \(\boldsymbol{\epsilon }\)-Nash Equilibrium seeking problem subject to external disturbance. The game is played by multi-agent with two order integrators under full information. In order to estimate and remedy external disturbance, a static extended stubborn state observer is proposed. An \(\boldsymbol{\epsilon }\)-Nash Equilibrium seeking strategy is proposed to regulate the action of each agent to around Nash Equilibrium points regard to full information. Finally, a numerical example is presented to verify the validity of the proposed \(\boldsymbol{\epsilon }\)-Nash equilibrium seeking method.