Variable-Exponent Sliding Mode Control of Input-Constrained Systems: Application to Spacecraft Attitude Regulation

This study proposes a predefined-time sliding mode control framework for Lagrangian systems subject to input constraints, which is singularity-free and chattering-free. The favorable performance stems from the use of a state-dependent variable exponential approach and a smooth hyperbolic tangent function. A smooth sliding surface based on a state-dependent variable exponential predefined-time formulation is established. A smooth reaching law with state-dependent variable exponent is designed and incorporated into the controller synthesis, to suppress chattering and ensure robust stabilization of the closed loop dynamics within a predefined time. To address saturation nonlinearity, an auxiliary predefined-time subsystem is devised. Through rigorous theoretical analysis, the proposed scheme is devoid of singularities and guarantees predefined-time convergence of the controlled system. Finally, the developed control methodology is implemented in a spacecraft attitude regulation problem, and numerical simulations confirm its effectiveness.