Neural-Network-Based Adaptive DSC Design for Switched Fractional-Order Nonlinear Systems

Abstract

Due to the particularity of the fractional-order derivative definition, the fractional-order control design is more complicated and difficult than the integer-order control design, and it has more practical significance. Therefore, in this article, a novel adaptive switching dynamic surface control (DSC) strategy is first presented for fractional-order nonlinear systems in the nonstrict feedback form with unknown dead zones and arbitrary switchings. In order to avoid the problem of computational complexity and to continuously obtain fractional derivatives for virtual control, the fractional-order DSC technique is applied. The virtual control law, dead-zone input, and the fractional-order adaptive laws are designed based on the fractional-order Lyapunov stability criterion. By combining the universal approximation of neural networks (NNs) and the compensation technique of unknown dead-zones, and stability theory of common Lyapunov function, an adaptive switching DSC controller is developed to ensure the stability of switched fractional-order systems in the presence of unknown dead-zone and arbitrary switchings. Finally, the validity and superiority of the proposed control method are tested by applying chaos suppression of fractional power systems and a numerical example.