Design of an adaptive fixed-time control for a class of second-order nonlinear systems using sliding mode control

This paper addresses the problem of fixed-time control for a class of second-order nonlinear systems in the presence of model uncertainty and external disturbance. By introducing a novel form of non-singular terminal sliding mode control, a fixed-time control is designed to obtain acceptable performance, rapid convergence of the system states, high robustness and singularity elimination. Guaranteeing fixed-time convergence is a significant feature of the proposed control law under which the convergence time of the proposed surface is independent of the initial conditions. Since the upper bound of the system uncertainty and disturbance is quite difficult to obtain, an adaptive mechanism is presented under which there is no need to know this upper bound. Lyapunov analysis proves that the system states converge to small neighborhood of the origin within a fixed time. To assess efficiency of the suggested method, a flexible spacecraft attitude control system is considered and a fixed-time attitude control system is derived. Simulation results verify the effectiveness and performance of the presented approach.