Sliding Mode Control Design for a Class of Nonlinear Fractional Systems with Application to Glucose-Insulin Systems

Abstract

These days analysis and research about the nonlinear fractional system (NFS)s in the presence of uncertainty and external disturbance is one of the most critical problems in the control field. This paper investigates the asymptotic stabilization of a class of NFS while the upper bound of uncertainty and external disturbance are unknown. To do this, first, a fractional-integral sliding surface is constructed. After that, a new robust adaptive fractional sliding mode controller (RAFSMC) is designed, which is robust against the model uncertainties and external disturbances. The unknown upper bound of uncertainties and disturbances is estimated by a stable adaptive law. The Lyapunov stability theorem is used for stability analysis of the designed controller. Finally, the proposed method is applied to two practical examples, the glucose-insulin and the Lu systems. The simulation results are provided to show the effectiveness of the proposed methodology. These examples show rapid convergence to the equilibrium point with low chattering.

Keywords

• sliding mode control
• nonlinear fractional systems
• glucose-insulin system