Prescribed-time formation control considering delay effects based on enhanced sliding modes and composite learning

During the dynamic formation reconfiguration process, to meet the real-time requirements of dynamic missions while addressing the coupled challenges of time delays and uncertainties, this paper proposes a formation control strategy that compensates for input delays and guarantees convergence in a predefined time. Firstly, to address the destabilizing effects of input delay, a state predictor is designed and stability conditions are rigorously derived using Lyapunov-Krasovskii theory, ensuring robustness against delay-induced performance impact. Secondly, building on second-order UAV dynamics, a novel prescribed-time sliding mode control (PTSMC) law is developed. Theoretical proofs demonstrate the stability of this control law, which empowers each UAV to converge precisely to its designated position within the predefined time order, and effectively suppressing chattering through the optimized sliding surface design. Thirdly, to handle system uncertainties, a compound learning is integrated within the PTSMC framework. By incorporating prediction and tracking errors into adaptive weight updates, the scheme enhances estimation accuracy and improves its performance in the face of uncertainties. Finally, comprehensive simulations validate the algorithm's efficacy, demonstrating superior performance in formation tracking under delays and uncertainties. This work advances the practicality of multi-UAV cooperative control, offering a robust solution for real-world deployment.