Finite-Time Stabilization of the Fractional Model of the Driven Dissipative Nonlinear Pendulum

Abstract

Finite-time stabilization of the driven dissipative nonlinear pendulum is investigated in this paper. First, asymptotic and nonasymptotic convergence towards stable and unstable orbits of the ordinary model of the driven dissipative nonlinear pendulum is considered. It is shown that the existence of nonasymptotic convergence does not contradict the fact that time-reversal invariance holds true for the ordinary model of the driven dissipative nonlinear pendulum. Then, finite-time stabilization of unstable orbits of the fractional model of the driven dissipative nonlinear pendulum is discussed. The proposed stabilization technique is based on a proper selection of initial conditions and does not require any feedback loops. Computational experiments are used to illustrate the efficacy of the proposed finite-time stabilization techniques.