Finite and Fixed-Time State Estimation: Pendulum-Cart System

In this paper the problem of state estimation for the Pendulum-Cart System is addressed. Different high-order sliding-modes techniques are applied for such a mechanical system. The mathematical model is studied and a couple of high-order sliding-modes observers are proposed to estimate the state, in spite of disturbances; exactly and in a finite or fixed-time, respectively. Some experiments and comparisons are presented to illustrate the effectiveness of the presented algorithms.