Finite-time Backstepping for Attitude Tracking with Disturbances and Input Constraints

Backstepping (BS) is an important framework to stabilize the high-order nonlinear system. This work develops a finite-time convergence property for the BS framework combined with an auxiliary input saturation compensator and applies it to address attitude tracking problem of a rigid body subjected to disturbances and input constraints. The finite-time convergence of the tracking error is guaranteed by introducing the fractional power of tracing errors. Meanwhile, the finite-time filters of the target commands and the finite-time disturbance observers inspired by multivariable super-twisting algorithm are employed to construct the finite-time BS framework. Another novelty is to propose a novel auxiliary system to handle the adverse effect of input saturation. The singularity of auxiliary dynamics is avoided by the cubic representation of auxiliary variables. Attitude tracking errors are demonstrated to converge to zeros in finite time despite the presence of input saturation and disturbances through Lyapunov theory. Comparative simulations are conducted to demonstrate the effectiveness and superiority of the proposed control system.