Fractional finite-time control for robust tracking of nonlinear systems subject to Hölder disturbances with application to UAVs

The aim of the present article is to design a robust fractional-order (FO) finite-time (FnT) control able to tackle Hölder disturbances of second-order nonlinear systems. First, a novel sliding manifold with Arc-Tangent function is suggested for second nonlinear systems. It has been proven that the system states globally converge to the origin in FnT using the proposed sliding mode variable. To ensure a FnT stability of the sliding variable, a robust control is developed. By using fractional operators, a uniformly continuous control law is designed to tackle Hölder disturbances. Furthermore, the suggested approach is shown to be resistant to matched Hölder disturbances and uncertainties that are continuous but not necessarily differentiable. Moreover, the FnT stability of quadrotors using the proposed control, that is our second result. The quadrotor simulations analysis demonstrates the practicality of the proposed FnT controller in the presence of Hölder disturbances.