Practically Predefined-Time Adaptive Sliding Mode Control for Non-Linear Systems via Time-Base Generators

This paper focuses on the practically predefined-time adaptive sliding mode tracking control for uncertain non-linear systems using time-base generator (TBG) methods. Firstly, a novel and non-singular predefined-time sliding variable, which consists of a TBG and a hyperbolic tangent function, is proposed. In the sliding phase, the TBG ensures that the tracking error achieves practical predefined-time convergence, while the hyperbolic tangent function guarantees that the tracking error converges to an adjustable region that is not explicitly related to the convergence bound of the sliding variable. Secondly, a special case of TBG is adopted to construct an auxiliary variable that guarantees the practical predefined-time convergence of the sliding variable in the reaching phase. In the controller design, the radial basis function neural network (RBF NN) is used to approximate the lumped disturbance. Moreover, the inverse of the class-$𝒦$ function is utilized as the control gain of the sliding mode controller to deal with the reconstruction error of the RBF NN and to predefine the convergence bound of the sliding variable. Finally, digital simulations are conducted by using an unmanned surface vehicle to demonstrate the validity of the theoretical results.