Fixed-Time Quasi-Consensus and Quasi-Containment Control for Multi-Agent Systems Under Non-Periodic Unknown DoS Attacks

This study investigates the fixed-time quasi-consensus and quasi-containment control for multi-agent systems (MASs) under non-periodic unknown denial-of-service (DoS) attacks. Most available strategies fail to construct fixed-time observers and feasible corresponding parameter tuning rules to guarantee the precise fixed-time convergence of observer states to the convex hull trajectory spanned with multiple leaders under arbitrary non-periodic DoS interference. Moreover, most existing relevant fixed-time cooperative control methods for MASs commonly impose restrictive assumptions on system input matrices, requiring the matrix to be square and invertible, which severely limits their practical applicability. To overcome these limitations, the observers and corresponding parameter selection conditions are designed in this study, which can ensure that the observer states converge to the target trajectory formed by the leaders within a fixed time under non-periodic unknown DoS attacks. Then, based on the linear transformation of the state space and the theory of sliding mode control, a novel observer-based controller is proposed to solve the fixed-time quasi-consensus and quasi-containment control problems. The proposed approach remains effective even when, under mild conditions, the input matrix is non-square or non-invertible—a challenge that many existing methods cannot address. Finally, numerical simulations demonstrate that the proposed control strategy enables MASs with non-square input matrices suffering from unknown non-periodic DoS attacks to achieve fixed-time quasi-consensus and quasi-containment under mild conditions.