Adaptive Continuous Sliding Mode Control for Fractional-order Systems with Uncertainties and Unknown Control Gains

The main purpose of this paper is to design the continuous sliding mode control, which resolves the stability problem of fractional-order nonlinear systems by taking into consideration both matched and unmatched uncertainties, and unknown control gains. Three different sliding mode controllers are put forward to attenuate the chattering problem, which pass an adaptive fractional-order filter. The control function constituted of a novel SMC method and backstepping control is proposed to deal with the problem of unmatched uncertainty. Utilizing the fractional-order Lyapunov technology and the finite-time control strategy, the analysis results of this paper are theoretically proved. Finally, the availability and feasibility of the suggested chattering free sliding mode control are also confirmed by the application to the control of the fractional-order horizontal platform system.