Optimal Time-Varying Formation Tracking Control for Heterogeneous Nonlinear HFV Swarms with Uncertain Dynamics and Disturbances

This paper investigates the optimal time-varying formation tracking control (TVFTC) problem for a heterogeneous swarm of hypersonic flight vehicles (HFVs) with a non-cooperative leader. Conventional approaches often fail to achieve both precise TVFT and optimal performance under multiple uncertainties. To address these limitations, a novel integrated control scheme, incorporating an adaptive neural network and an Extended State Observer (ESO), is proposed. First, an ESO enhanced by an adaptive neural network is designed to accurately estimate and compensate for the aggregated uncertainties in real time. Second, based on this observer, a distributed optimal TVFTC protocol is constructed, which eliminates the need for intermediate control laws. Then, by leveraging the Lyapunov stability theory, it is rigorously proven that the closed-loop system can achieve the predefined formation tracking objectives while maintaining optimal control performance, despite the presence of uncertainties. Finally, numerical experiments were performed to verify the efficacy of the developed control scheme.