Abstract

Abstract

This study addresses the containment control challenge in heterogeneous, nonlinear fractional-order multi-agent systems (MASs) operating under uncertainties, actuator faults, unknown nonlinearities, and mixed timevarying delays, with the aim of ensuring stability and robust performance in realistic environments. A fully distributed adaptive observer is developed for each follower to estimate leader state information using only local neighbor data, and an interval type-2 fuzzy logic system is integrated into the adaptive control law to approximate unknown dynamics and compensate for actuator faults. Stability is established via a newly formulated fractional-order Lyapunov Krasovskii functional combined with inequality analysis, and the method’s effectiveness is verified through simulations on a fractional-order Lorenz-based MAS. Results show that the proposed approach achieves precise containment control despite actuator efficiency loss and bias faults, with an root-mean-square error (RMSE) of 0.028, a settling time of 1.2 s, and disturbance rejection within 0.8 s, outperforming classical Proportion, Integral, Differential (PID) and Type-1 fuzzy controllers. These findings demonstrate that the proposed framework not only enhances fault tolerance and tracking accuracy but is also computationally efficient, making it suitable for real-time applications such as UAV swarms, autonomous vehicles, and cooperative robotics.OPEN ACCESS Received: 12/11/2025 Accepted: 22/12/2025