Predefined time adaptive controller design for attitude synchronisation of chaotic satellites with unknown effects

This study proposes a practical predefined-time adaptive control framework for the synchronisation and anti-synchronisation of chaotic satellite attitude dynamics subject to unknown nonlinearities, parametric uncertainties, and bounded external disturbances. The proposed controller combines radial-basis-function (RBF) neural-network approximation of lumped unknown dynamics with adaptive estimation laws for both physically meaningful satellite parameters and neural-network weights. A Lyapunov-based stability analysis proves that all closed-loop signals remain bounded and that the synchronisation errors converge to an explicitly characterised residual neighbourhood of the origin within a predefined upper-bound time independent of initial conditions. The residual bound is expressed in terms of the neural approximation error, adaptive gains, and predefined-time design parameters, thereby providing practical tuning insight. Comparative numerical simulations demonstrate that the proposed approach achieves fast convergence, reduced actuator effort, and improved robustness under varying inertia, disturbances, and initial conditions. These results indicate the suitability of the proposed method for satellite formation and attitude-control tasks requiring predictable convergence times and resilience to modelling uncertainties.