Review on the developments of sliding function and adaptive gain in sliding mode control

Sliding mode control (SMC) is a well-known robust nonlinear control method with strong robustness and fast response which has been widely used in many applications. This paper introduces the major results of SMC design methods that the authors have achieved in the last decade. Undoubtedly, our results are obtained based on many other researchers’ pioneer work in the literature which will not be discussed in detail here. Notably, our development has a main focus on tackling practical issues such that a proposed or enhanced SMC approach is effectively applicable to motion control systems. Issues on sliding function and adaptive gain designs in SMC and their control features will be both discussed in this paper. Those issues comprise fast convergent speed, predefined convergent time, input saturation restriction, chattering reduction, and unknown disturbance suppression. Lastly, conclusion and a few remarks on future research directions are presented. • The fast nonsingular terminal sliding mode (FNTSM) is reviewed such that finite-time convergence of the control system can be achieved. Moreover, the predefined-time sliding mode (PTSM) is developed based on a class K 1 function that can predefine the upper bound of the convergent time by a constant. • The leakage-type adaptive law guarantees finite-time convergence of the sliding variable to a region determined by the disturbance’s upper bound. For improvement, the class K -type adaptation predefines the size of the above region that is not associated with the disturbance’s upper bound.