A novel sliding surface design for predefined-time stabilization of Euler–Lagrange systems

Abstract

This paper gives a class of novel predefined-time sliding mode surfaces based on the time-regulator function, forcing the states on them to approach the origin in a predefined time, which can be employed to replace the linear sliding mode surface that is used in the existing literatures focused on the predefined-time set stabilization problems such that the zero-error predefined-time stability can be achieved. In this way, the settling time is independent of the initial conditions and can be explicitly predefined as a specific control parameter. Later, such sliding mode surfaces are utilized to construct the nonsingular sliding mode control (SMC) for both uncertain second-order systems and disturbed Euler–Lagrange systems. The sufficient conditions for the proposed control schemes to guarantee the predefined-time stability, satisfactory capability of disturbance rejection, and nonsingularity of the control input are derived through systematic stability analysis. Finally, several numerical simulations are performed on generalized uncertain second-order systems and 2-DOF (degree of freedom) robot manipulator to show the effectiveness and the performance of the presented control schemes.