Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities.

This study addresses the issue of the adaptive output tracking control for a category of uncertain nonstrict-feedback delayed incommensurate fractional-order systems in the presence of nonaffine structures, unmeasured pseudo-states, unknown control directions, unknown actuator nonlinearities and output constraints. Firstly, the mean value theorem and the Gaussian error function are introduced to eliminate the difficulties that arise from the nonaffine structures and the unknown actuator nonlinearities, respectively. Secondly, the immeasurable tracking error variables are suitably estimated by constructing a fractional-order linear observer. Thirdly, the neural network, the Razumikhin Lemma, the variable separation approach, and the smooth Nussbaum-type function are used to deal with the uncertain nonlinear dynamics, the unknown time-varying delays, the nonstrict feedback and the unknown control directions, respectively. Fourthly, asymmetric barrier Lyapunov functions are employed to overcome the violation of the output constraints and to tune online the parameters of the adaptive neural controller. Through rigorous analysis, it is proved that the boundedness of all variables in the closed-loop system and the semi global asymptotic tracking are ensured without transgression of the constraints. The principal contributions of this study can be summarized as follows: (1) based on Caputo's definitions and new lemmas, methods concerning the controllability, observability and stability analysis of integer-order systems are extended to fractional-order ones, (2) the output tracking objective for a relatively large class of uncertain systems is achieved with a simple controller and less tuning parameters. Finally, computer-simulation studies from the robotic field are given to demonstrate the effectiveness of the proposed controller.