Finite-Time Adaptive NN Backstepping Dynamic Surface Control for Input-Delay Fractional-Order Nonlinear Systems

This article focuses on a finite-time adaptive dynamic surface control (DSC) approach for a kind of nonstrict fractional-order nonlinear systems (FONSs) with input delay. An auxiliary compensation function is presented by using the integral function of the input signal to handle input delay problem. To overcome the problem of inherent computational complexity, a fractional-order filter is applied to approach the virtual controller and its fractional-order derivative in each step of the backstepping procedure. By using backstepping technology and neural network (NN), the finite-time adaptive DSC approach is developed, and finite-time stability criteria based on fractional-order Lyapunov method are introduced to prove the finite-time convergence of the tracking error into a small region around the origin. The effectiveness of the presented control scheme is demonstrated by two examples.