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Adaptive fast terminal sliding mode control for a class of nonlinear systems with time-varying uncertainties via LMI approach

This paper proposes an adaptive fast terminal sliding mode control for a class of multiple input nonlinear systems with time-varying mismatched uncertainties via LMI approach. First, a novel fast terminal sliding surface design method for a class of nonlinear systems is proposed based on Lyapunov method. The sufficient conditions are provided for the uncertain system on the sliding surface, such that the terminal sliding motion is finite stable. Second, the corresponding new adaptive reaching law is constructed based on the Lyapunov method, which can drive the state trajectory of the close-loop system onto the sliding surface within limited time. The chattering around the sliding surface can be allevated by the proposed approach. In addition, on-line adaptive laws of the control system are also derived based on the gradient descent method. Simulation results validate the effectiveness of the proposed control scheme for multiple input nonlinear systems with unknown uncertainties.