Distributed Containment Control for Caputo Fractional-Order Multi-Agent Systems Under Stochastic Communication Uncertainties and Intermittent DoS Attacks

The current paper deals with the containment control issue of fractional-order complex networks (FCNs) under communication uncertainties occurring with both multiplicative and additive noises and denial-of-service attacks. The dynamics of the followers are incorporated through the use of Caputo fractional derivatives, which are able to capture the nature of memory and hereditary dynamics of the complex systems. In order to reduce stochastic noise caused by the noisy communication medium, a new distributed containment protocol is proposed that takes both the multiplicative and additive noise effects in the interactions between the leader and the followers. Using the Mittag–Leffler stability theory, stochastic Lyapunov analysis, Itô calculus, the derivation of necessary conditions to ensure that the followers converge to the convex hull of the leaders was done. The explicit stability conditions are stipulated based on system parameters and control gains as well as intensities of noise. In addition, the robustness of the protocol suggested for use against intermittent DoS attacks is critically examined. The theoretical findings are substantiated by simulation experiments that demonstrate that the suggested methodology guarantees containment and resilience to the fluctuations in the fractional order and communication breakdowns. The findings offer an inclusive framework in the development of robust distributed controllers of fractional-order MASs operating under adversarial and uncertain networked frameworks.