Neuro-adaptive tracking control of non-integer order systems with input nonlinearities and time-varying output constraints

This paper studies the design of neuro-adaptive tracking control schemes for non-integer order non-square systems subject to time-varying output constraints and input nonlinearities. It should first be stated that by employing the mean-value theorem, the original non-affine non-square system with actuator nonlinearities is converted into an equivalent affine square form. Neural networks, Barrier Lyapunov Functions and Nussbaum functions are then incorporated to overcome the difficulties raised by the uncertain nonlinear dynamics, output constraints and unknown control directions, respectively. In a further step, in order to systematically derive the control signals and updating laws, the Backstepping technique is applied. It is shown that by using the proposed adaptive controller, the semi-global asymptotic tracking and the boundedness of all variables in the closed-loop system are guaranteed without transgression of the constraints. The foremost contributions of this paper include: (1) by means of new lemmas and corollaries based on Caputo fractional derivative definitions, techniques and approaches related to the stability analysis and controllability of integer-order plants are extended to fractional-order non-square ones, and (2) the ‘explosion of complexity’ issue is fixed. Finally, simulation results are provided to reveal the effectiveness of the proposed control scheme.