Chaotic behavior in fractional-order horizontal platform systems and its suppression using a fractional finite-time control strategy

The present paper investigates the dynamical properties of a non-autonomous fractional-order horizontal platform system (FOHPS). According to different parameter settings, we show that the FOHPS can possess stable, chaotic and unstable states. Using the maximal Lyapunov exponent criterion, we show that the FOHPS exhibits chaos. Strange attractors of the system are also plotted to validate chaotic behavior of the system. Since the chaotic behavior of the FOHPS may be undesirable, a fractional finite-time controller is introduced to suppress the chaos of the FOHPS with model uncertainties and external disturbances in a given finite time. We use the fractional Lyapunov theory to prove the finite time stability and robustness of the proposed scheme. Finally, computer simulations are given to illustrate the efficiency and applicability of the proposed fractional control method.