Neural Network Backstepping Controller Design for Fractional-Order Nonlinear Systems

In this work, a backstepping controller design for fractional-order strict feedback systems is investigated and the neural network control method is used. It is noted that in the standard backstepping design, the fractional derivative of the virtual quantity needs to be calculated repeatedly, which will lead to a sharp increase in the number of controller terms with the increase of the system dimension and finally make the control system difficult to bear. To handle the estimation error, certain robust terms in the controller at the last step are designed. The stability of the controlled system is proven strictly. In addition, the proposed controller has a simple form which can be easily implemented. Finally, in order to verify our theoretical method, the control simulation based on a fractional-order chaotic system is implemented.