Practical Predefined-Time Safe Resilient Consensus of Heterogeneous Nonlinear Fractional-Order Multi-Agent Systems Under Hybrid Cyber Attacks

This paper investigates safe leader-following consensus of heterogeneous nonlinear Caputo fractional-order multi-agent systems under simultaneous denial-of-service (DoS), sensor-deception, and actuator-deception attacks. A joint augmented observer reconstructs the local state and two deception channels, while a distributed predictor–corrector leader observer operates across normal and DoS intervals. An order-dependent average Mittag–Leffler increment condition is specialized to the considered DoS leader-observation dynamics, thereby avoiding an integer-order switching argument and memory resetting at switching instants. Explicit linear matrix inequalities are provided for the local observer gains, and certified all-time observer envelopes are propagated into a tightened barrier domain so that attack-reconstruction accuracy is quantitatively linked to the physical safety reserve. An innovation-compensated barrier controller with a deadline-dependent gain is then developed. For every initial condition in a prescribed compact safe set, a componentwise Mittag–Leffler inequality guarantees entry into an adjustable residual set no later than a designer-assigned time without claiming exact finite-time convergence of the Caputo state. Two main theorems establish bounded attack reconstruction, DoS-resilient observation, forward invariance of the physical safety set, and practical predefined-time consensus. The numerical study includes a five-follower benchmark, a three-grid refinement analysis, disturbance- and benchmark-gain sensitivity tests, certified post-deadline physical bounds, and a compact two-dimensional case with a nontrivial oscillatory leader for which the adverse-mode rate is strictly positive. These tests verify the observer LMI, analytical safety reserve, DoS condition, and deadline inequality.