Exponential consensus of stochastic discrete multi-agent systems under DoS attacks via periodically intermittent control: An impulsive framework

Abstract

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.