Parameters adaptive sliding mode control for a class of uncertain nonlinear systems

A sliding mode controller with the adaptive parameters is proposed for a class of uncertain nonlinear systems such that the sliding mode parameter lambda , the approximate sign function parameter mu , the tendency rate k₀ and the gain parameter eta be scheduled by the system states. Meanwhile, the obtained systems have the desired stable sliding mode motions with the appropriate parameters lambda mu , k₀, eta. The constructed parameters adaptive laws are shown to be convergent with the Lyapunov stability theory, and the sliding mode is shown to be stable. The simulation results are given to show the specialties of the proposed method, such as low cost, no-strong control signal varying extent and so on.