This article is devoted to investigating the exponential leader-following consensus (ELFC) of stochastic discrete multi-agent systems (SDMASs) in the presence of parameter uncertainties, nonlinearities, stochastic disturbances and denial-of-service (DoS) attacks. A novel control strategy, namely, periodically intermittent impulsive control (PIIC), is designed to cut down unnecessary communication costs and maintain the well-pleasing performance, where the impulsive instants only appear at control windows. Specifically, we explore the ELFC of SDMASs without DoS attacks via the PIIC strategy. The relation among the control period, the control width and the impulsive interval is derived by mean of utilizing the Lyapunov method and the linear matrix inequality technique. Besides, for SDMASs under DoS attacks, the following results are obtained: 1) under reasonable assumption that adversaries fail to work persistently within given intervals, a sufficient criterion is derived to ensure the ELFC of SDMASs; 2) the control rate is derived associated with the impulsive interval, the impulsive gain, the DoS attack ratio and the attack intensity; and 3) the novel protocol can achieve ELFC and cut down control costs effectively. More interestingly, a novel concept of periodic window-based average impulsive interval is proposed to make our developed criteria less conservative. Finally, simulation examples are demonstrated to certify the applicability of PIIC and the effectiveness of our main results.

本文致力于研究在存在参数不确定性、非线性、随机干扰和拒绝服务 (DoS) 攻击的情况下随机离散多智能体系统 (SDMAS) 的指数领导者跟随共识 (ELFC)。一种新颖的控制策略，即周期性间歇脉冲控制（PIIC），旨在减少不必要的通信成本并保持良好的性能，其中脉冲瞬间仅出现在控制窗口中。具体来说，我们通过 PIIC 策略探索了没有 DoS 攻击的 SDMAS 的 ELFC。利用Lyapunov方法和线性矩阵不等式技术推导了控制周期、控制宽度和脉冲间隔之间的关系。此外，对于受到 DoS 攻击的 SDMAS，得到以下结果：1) 在对手无法在给定时间间隔内持续工作的合理假设下，推导出一个充分的标准来确保 SDMAS 的 ELFC；2) 控制率与脉冲间隔、脉冲增益、DoS攻击率和攻击强度相关联；3）新颖的协议可以实现ELFC，有效降低控制成本。更有趣的是，提出了一种基于周期性窗口的平均脉冲间隔的新概念，以使我们开发的标准不那么保守。最后，通过仿真实例证明了 PIIC 的适用性和我们主要结果的有效性。2) 控制率与脉冲间隔、脉冲增益、DoS攻击率和攻击强度相关联；3）新颖的协议可以实现ELFC，有效降低控制成本。更有趣的是，提出了一种基于周期性窗口的平均脉冲间隔的新概念，以使我们开发的标准不那么保守。最后，通过仿真实例证明了 PIIC 的适用性和我们主要结果的有效性。2) 控制率与脉冲间隔、脉冲增益、DoS攻击率和攻击强度相关联；3）新颖的协议可以实现ELFC，有效降低控制成本。更有趣的是，提出了一种基于周期性窗口的平均脉冲间隔的新概念，以使我们开发的标准不那么保守。最后，通过仿真实例证明了 PIIC 的适用性和我们主要结果的有效性。