Fast finite time fractional-order robust-adaptive sliding mode control of nonlinear systems with unknown dynamics

Abstract

This study investigates the fast finite-time robust-adaptive terminal sliding-mode control of nonlinear affine high order (NAHO) systems based on fractional-order control approach. It is considered in this paper that dynamic parameters of the nonlinear system are completely unknown. To do this, at first a high-order fractional order sliding surface is proposed. Then, considering that there is no any information about dynamics of system due to the large amount of uncertainties and unmolded dynamics, a finite-time fractional-order adaptive sliding-mode controller is devised to achieve finite-time stability with quick convergence of system output to its desired trajectory. A stable adaptive law is also designed to estimate the system’s unknown dynamic parameter vector. This is worth to mention that using the designed control law, finite time convergence is obtained in a more real condition where the dynamic parameters of the system are unknown and because of using a fractional order sliding surface, the chattering phenomena is less than ordinary terminal sliding mode controller. The developed Lyapunov theory has been employed to prove the stability of the closed-loop system. The simulation results are demonstrated on a cable robot with unknown dynamics to validate the effectiveness of the control law.