Abstract

This paper studies resilient safe distributed optimization with practical prescribed-time performance for fractional-order multi-agent systems under false data injection attacks. Caputo dynamics are used to represent memory-dependent agent behavior. A local trimming mechanism is combined with gradient feedback, auxiliary coordination, a bounded time-varying gain, and a barrier-type safety correction. In contrast to an ideal singular prescribed-time design, the proposed bounded gain drives the normal-agent errors into an explicitly characterized neighborhood of the global optimizer at the assigned time, provided that a verifiable gain matrix is positive definite. Explicit residual bounds are derived in terms of the attack amplitudes, the trimming level, and the retained-neighbor redundancy. A fractional extremum argument is further used to establish forward invariance of the safe interval. The analysis proves boundedness of the physically relevant closed-loop signals, safety preservation, practical prescribed-time convergence, and robustness against bounded disturbances. Simulations on a sparse six-agent network demonstrate the roles of resilient information processing and barrier correction without requiring all-to-all communication.

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