Neuro-adaptive fractional order prescribed performance backstepping control for a class of strict-feedback non-linear systems

To suppress the non-linear motion for a class of strict-feedback fractional order non-linear systems, and to improve their transient and steady-state performance, a neuro-adaptive prescribed performance backstepping control strategy suitable for a class of strict-feedback non-linear systems is proposed in this paper. Firstly, the interval Type-2 fuzzy neural network is constructed to approximate the unknown non-linear functions. Secondly, the tracking differentiator is introduced to address the problem of ‘explosion of complexity’ associated with the technique framework of backstepping. Then, a prescribed performance backstepping controller composed of predetermined performance functions and equivalent transformed errors, which can ensure that the tracking errors converge with the predetermined performance intervals for a class of strict-feedback non-linear systems, is designed within the technique framework of backstepping control. Finally, the stability analysis, two simulation experiments and comparative experiment results are presented to demonstrate the feasibility and effectiveness of the designed controller.