Dynamic event-triggered adaptive control for zero-sum games of nonlinear stochastic systems

Abstract

This paper considers solving the zero-sum games (ZSGs) of nonlinear stochastic systems under the architecture of dynamic event-triggered mechanism (DETM). The adaptive dynamic programming (ADP) approach with great approximate computing power is proposed to seek the saddle-point equilibrium solution of ZSGs. First, the Hamilton–Jacobi–Isaacs equation of stochastic version is constructed which is the key to solving the two-player ZSGs. Then, the ADP method is employed to search the approximated solution under the dynamic triggering mechanism. On the foundation of static event-triggered mechanism (SETM), the DETM is derived through introducing an internal dynamic invariable to further lower the update frequency for the strategies. Additionally, the stability of the closed system is demonstrated in detail via the Lyapunov theory. Finally, two representative examples are provided to present the availability and reliability of this approach from different perspectives.