Neural network ℒ1 adaptive control for a class of uncertain fractional order nonlinear systems

This research work presents an ℒ1 adaptive control scheme based on a fractional-order sliding surface and a Radial Basis Function (RBF) neural network, for a general class of uncertain fractional-order nonlinear systems. The structure of the proposed controller is composed of a predictor, a control law, an adaptive mechanism and an RBF neural network. The latter is designed as an estimator in the controller architecture to handle and approximate nonlinear uncertain dynamics. The estimation loop in the proposed Neural Network (NN) fractional-order ℒ1 adaptive controller is decoupled from the control loop thanks to the use of a filter in the input channel, which makes it possible to preserve the robustness while enhancing transient performances. Besides, the suggested controller guarantees the closed-loop system’s stability with bounded transient and tracking performances. Finally, the effectiveness and efficiency of the proposed controller are put on test using numerical simulations and comparative studies.