Abstract

The paper presents a resilient dynamic adaptive event-triggered sliding mode control (DAET–SMC) framework for fractional-order delayed multi-agent systems under actuator saturation, stochastic disturbances, and cyber-attacks. Existing methods often fail to ensure containment and formation stability when multiple practical constraints coexist. The proposed approach leverages Riemann–Liouville fractional dynamics to capture system memory effects and integrates adaptive compensation to mitigate actuator faults, measurement attacks, and communication delays. Numerical simulations on a 16-agent network with one leader and fifteen followers show that all followers achieve containment within 20 s, with formation errors below 10−2m, while maintaining bounded control effort. Compared with conventional non-adaptive controllers, the proposed method demonstrates faster convergence, superior robustness, and resilience under combined disturbances, achieving up to 35% faster error convergence and maintaining control input within saturation limits. These results confirm the effectiveness of the DAET–SMC strategy for practical multi-agent coordination in uncertain and constrained environments.OPEN ACCESS Received: 30/10/2025 Accepted: 26/11/2025

Abstract

The paper presents a resilient dynamic adaptive event-triggered sliding mode control (DAET–SMC) framework for fractional-order delayed multi-agent systems under actuator saturation, stochastic disturbances, and cyber-attacks. Existing methods often fail to ensure containment and formation stability when multiple practical constraints coexist. The proposed approach leverages Riemann–Liouville fractional dynamics to capture system memory effects and integrates adaptive compensation to mitigate actuator faults, measurement attacks, and communication delays. Numerical simulations on a 16-agent network with one leader and fifteen followers show that all followers achieve containment within 20 s, with formation errors below 10−2m, while maintaining bounded control effort. Compared with conventional non-adaptive controllers, the proposed method demonstrates faster convergence, superior robustness, and resilience under combined disturbances, achieving up to 35% faster error convergence and maintaining control input within saturation limits. These results confirm the effectiveness of the DAET–SMC strategy for practical multi-agent coordination in uncertain and constrained environments.OPEN ACCESS Received: 30/10/2025 Accepted: 26/11/2025 Published: 23/01/2026

Abstract

In this paper, the issue of distributed containment control for multiple Unmanned Aerial Vehicles (UAVs) is discussed using a fractional-order model with convenient limitations. A new event-based finite-time slidingmode control algorithm is proposed to enable the follower UAVs to converge to the convex hull spanned by a set of dynamic leaders. The suggested approach is immune to actuator failure, input constraint, timevarying communication delays, as well as exogenous stochastic disturbances. Memory effects present in UAV dynamics are reflected in the control law since fractional calculus is involved in calculations. The eventtriggering mechanism is configured to reduce the communication burden and ensure stability and performance. The convergence is verified carefully in finite time via Lyapunov techniques and the fractional stability of systems. It is ascertained that the proposed control scheme is highly effective and robust, as demonstrated by numerical simulations. The numerical simulations demonstrate that the proposed fractional-order fault-tolerant containment controllers achieve rapid convergence, with the average follower tracking error reducing below 0.02 within 5 s, and the multi-UAV formation remaining stable under stochastic disturbances and input saturation. These results highlight the effectiveness and robustness of the proposed strategies in maintaining desired containment performance across all agents.OPEN ACCESS Received: 09/11/2025 Accepted: 04/01/2026

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