Predefined-time control of nonlinear systems: A sigmoid function based sliding manifold design approach

Abstract

This work addresses the predefined-time convergence problem for a class of second order nonlinear systems subjected to matched disturbances. A novel family of sigmoid function based terminal sliding surfaces is proposed for which robust fixed time convergence is guaranteed. The stability properties are established through the Lyapunov framework. In the proposed technique, bound on the settling time is user-defined for arbitrary initial conditions. Furthermore, switching control law is designed to avoid singularity, thus sufficient condition for singularity free controller is determined. The utility of proposed control scheme is validated by simulating two numerical examples from recent relevant literature.

Keywords

• Arbitrary time control
• Fixed time stability
• Predefined settling time
• Preassigned-time convergence
• Sigmoid sliding surface
• Terminal sliding mode control