Fixed-time stabilization of second-order systems with unknown nonlinear inherent dynamics

This paper studies the fixed-time stabilization control for a class of second-order systems with unknown nonlinear dynamics and external disturbance. To achieve the fixed-time stability, two polynomial feedbacks, one with fractional exponent and the other with exponent greater than 1, are exploited in the sliding surface design. Then, considering the unknown nonlinear dynamics and the external disturbance, the unit-vector technique, coupled with the upper bounds related to the Lipschitz condition of nonlinear dynamics and the uncertain disturbance, is utilized to the fixed-time stability controller based on the designed sliding surface function. Finally, a forced pendulum system is used as case study example to examine the effectiveness of the developed design framework.