FTESO‐Based Finite Time Control for Underactuated System Within a Bounded Input

Finite time control problem is investigated for a class of underactuated systems with uncertainties and external disturbances. For the sake of expanding control region furthest within a bound input, finite time extended state observer (FTESO) and a novel adaptive terminal sliding mode (ATSM) controller are applied to improve the stability performance of system. Compared to the general extended state observer (ESO), FTESO makes use of fractional powers to reduce the estimation errors to zero in finite time. The coordinate transformation is made for more degrees of design freedom. Rigorous analysis of finite time convergence results has been performed through Lyapunov theory and sufficient conditions are provided for the observer/controller-design. Finally, simulation results on the Rotating Inverted Pendulum are given to demonstrate the effectiveness of the proposed controller and observer.