Saturation-Aware Containment Strategy for Fractional-Order Multi-agent Systems under Stochastic Perturbations and Delays

This article addresses the problem of containment control of fractional-order multi-agent systems (FOMASs) subject to practical restrictions, such as actuator saturation, stochastic perturbations, and communication delays. A new delay-margin-based control framework is proposed to examine and improve the robustness and stability of containment strategies. To handle nonlinearities, stochastic effects, and time-varying delays, an adaptive control scheme is synthesized using the fractional-order system dynamics and observer-based compensation. The proposed control protocol guarantees the asymptotic convergence of follower agents to the convex hull generated by multiple leaders, regardless of actuator constraints and random disturbances. Saturation-aware compensation and stochastic modeling ensure resilience against adverse cyber-physical perturbations. Lyapunov-based fractional calculus techniques are used to analyze stability and convergence rigorously. Long simulation studies are provided to confirm the theoretical results and demonstrate the effectiveness and robustness of the proposed containment method under various uncertain scenarios.