Fast finite-time backstepping for helicopters under input constraints and perturbations

This work addresses the issue of trajectory tracking of helicopters under disturbances and input constraints via the proposed fast finite-time backstepping framework. Backstepping with the property of fast finite-time convergence exhibits fast transient convergence both at a distance from and at a close range of the equilibrium. Moreover, finite-time disturbance observers based on multivariable super-twisting are employed to counteract the effect of perturbations. Aiming at the adverse effect of input saturation, a novel auxiliary system is developed to avoid the singularity by transforming auxiliary variables for three times. In addition, the framework is also applied into helicopter control problem, in which thrust magnitude and thrust direction are used as intermediate control variables, connecting external translational dynamics and internal angular dynamics. A rigorous proof of finite-time stability of the closed-loop system is derived from Lyapunov theory. Finally, the effectiveness and superiority of the proposed framework are verified by comparative simulation.