Finite-time Neural Network Adaptive Sliding Mode Control of Fractional-Order Chaotic Systems With Disturbance Observer And Fractional Robust Differentiator

This paper proposes a neural network adaptive sliding mode control scheme with a fractional-order disturbance observer and a robust differentiator for fractional-order chaotic systems with uncertain functions and random noise. The solution combines fractional-order differential controllers, gradient descent neural networks, and fractional-order disturbance observer techniques. A gradient descent neural network handles uncertain nonlinear functions, while fractional-order disturbance observers are presented to solve unexpected noise problems. On the premise that the above problems are solved, the state vector is used as the original signal, the ideal function as the tracking signal, and the design error function as the sliding mode surface. Meanwhile, in order to eliminate the vibration caused by the sliding mode functions, a fractional order robust differential observer is introduced in the estimation error. Adaptive rates are introduced in the design of the controller so that the control converges to a small interval in a finite time.