A global time-varying sliding-mode control for the tracking problem of uncertain dynamical systems

In this paper, a global time-varying sliding-mode control scheme with prespecified convergence time is proposed for the tracking problem of a class of uncertain nonlinear systems under parameters uncertainties and external disturbances. Firstly, a novel time-varying sliding manifold with appropriate coefficients is presented. These coefficients are tuned to eliminate the reaching phase and to drive the system states to the equilibrium in a specified time. Hence, the system states are constrained to the sliding surface from the beginning of the motion which enables the global robustness, the reduction of the initial control effort, and the meet of the convergence time requirement. Moreover, in order to address the more practical case that the upper bound of the system uncertainties and disturbances is unavailable, an adaptive time-varying sliding mode control algorithm is derived, by which the tracking error vanish as time tends to infinity. The stability of the system has been proved by the Lyapunov stability theorem, and simulation studies are conducted to show the effectiveness of the suggested control schemes.