Smooth attitude stabilisation in prescribed time of a rigid body despite uncertainties in inertia and additive disturbances

We consider the problem of stabilisation in predefined, finite time of the attitude of a rigid body. Inspired by classical laws in missile guidance, the proposed control law is time-varying but smooth as opposed to classical sliding-mode-based laws that are generally discontinuous, or continuous at best, and suffer from robustness issues. Through a backstepping design, and the explicit construction of a strict Lyapunov function, we are able to ensure stabilisation to a desired attitude even in the presence of uncertainties in the inertia matrix and under the effect of additive disturbances. Numerical simulations show the efficiency of the proposed controller.