Differential Game-Based Event-Triggered Impulsive Control for Disturbed Dynamical Systems
研究了一类受外部扰动的动态系统的博弈脉冲控制问题，设计了一种与哈密顿函数相关的无Zeno事件触发机制，将脉冲控制与微分博弈结合，在零和脉冲博弈框架下分析了稳定性并得到了纳什均衡解。
This article investigates the game-based impulsive control problem for a class of dynamical systems subject to exogenous disturbances. Particularly, a novel Zeno-free event-triggered mechanism (ETM) related to Hamiltonian functions is designed to determine the impulse frequency for optimality and helps to build a bridge between impulsive control and differential game. Utilizing event-triggered impulsive control (ETIC) technique, the stability performance analysis and Nash equilibrium setting are synthesized under the framework of zero-sum impulse game. First, some sufficient conditions for achieving${\mathcal {L}}_{2}$stability are provided via transforming impulsive control issue into zero-sum impulse game. Second, the Nash equilibrium solution containing an optimal impulsive control strategy and worst case disturbance policy is obtained underETICmethod. Moreover, the stability is analyzed for the systems under the derived equilibrium strategies. Finally, the effectiveness of the constructed impulsive control scheme and equilibrium strategies is validated through substantial simulations on practical systems.