Nonsingular Terminal Sliding Mode Control with Unknown Control Direction

This paper considers a nonsingular sliding mode controller for a second order system without a priori knowledge of the control direction. A novel nonsingular terminal sliding hypersurface is presented to adapt to the challenges of unknown control direction and avoid singularity issues at the origin. In contrast to the Nussbaum gain, where the equilibrium point is reached asymptotically, or the classical linear hypersurface, where the states are reached exponentially, the control structure in this paper guarantees that the states are reached in finite time. Additionally, the control algorithm is bounded and globally finite time stable in the presence of input matrix uncertainty and exogenous disturbance. Simulation results are provided to demonstrate the robustness of the developed control algorithm.