Fuzzy Distributed Observer-Based Containment Control for Nonlinear Fractional-Order Multi-Agent Systems with Mixed Time-Varying Delays and Cyber Attack Resilience

This paper addresses the critical problem of secure containment control for fractional-order heterogeneous and nonlinear multi-agent systems (MASs) subjected to both mixed time-varying delays and malicious false data injection. Such issues are highly relevant in modern networked control systems where data integrity and robustness are increasingly threatened. Within a leader–follower framework, the attacker injects unknown, time-varying, and deceptive signals that can compromise consensus and system stability. To counteract this, we propose a novel distributed observer and adaptive fuzzy-based feedback controller design for each agent. The observer accurately estimates the agents' states despite false data, while the controller ensures convergence and robustness under heterogeneous dynamics and delays. Stability of the closed-loop system is rigorously analyzed using a Lyapunov–Krasovskii functional tailored to fractional-order systems. Finally, simulation results demonstrate the effectiveness and resilience of the proposed control strategy against adversarial attacks.