Prescribed and controlled finite-time convergence based on a disturbance observer for an adaptive sliding mode controller

This paper proposes a method based on Lyapunov theory to guarantee a definite exact convergence time for an adaptive sliding mode controller applied to a class of nonlinear uncertain systems subject to bounded perturbations. To achieve the objective, the gain adaptation law is enhanced with a sliding mode disturbance observer. The new control scheme ensures the sliding variable follows the defined segment-like trajectory during the reaching phase, thereby reducing the necessary control signal amplitude by avoiding the overestimation of the control gains. This novel approach allows a reduction of the design constraints on the system actuators while guaranteeing an exact desired convergence time under unknown bounded perturbations. The disturbance observer tuning methodology is also addressed in function of the expected perturbation signal type. To support the proposition, numerical simulations are performed to illustrate the fixed-time disturbance rejection capacities of the closed-loop system subject to constant, periodic, or stochastic perturbations on a tutorial example. Finally, the proposed controller is applied to drive the velocities of an unmanned surface vehicle model under realistic perturbations.