A dynamic extremum seeking scheme for three-player attack-defense with unknown gradient

In this paper, a dynamic extremum seeking scheme is designed for a class of three-player attack-defense problems with unknown gradient, where an attacker intends to strike a non-maneuverable headquarters, while a defender attempts to prevent this attack. Firstly, a kinematic equation is utilized to model the defender's patrolling algorithm based on the law of gravitation. Then, a gradient estimation algorithm is employed to obtain derivatives of performance functions. In virtue of the Lyapunov function method, sufficient conditions are derived to guarantee the asymptotical stability of the closed-loop dynamic extremum seeking system. Finally, a group of simulations on wheeled mobile robot systems are exploited to illustrate the effectiveness of the proposed extremum seeking scheme.