Fault-tolerant adaptive fractional controller design for incommensurate fractional-order nonlinear dynamic systems subject to input and output restrictions

In this article, a fault-tolerant adaptive neural network fractional controller has been proposed for a class of uncertain multi-input single-output (MISO) incommensurate fractional-order non-strict nonlinear systems subject to five different types of unknown input nonlinearities, infinite number of actuators failures and arbitrary independent time-varying output constraints. The barrier Lyapunov function (BLF)-based backstepping technique and fractional Lyapunov direct method (FLDM) have been used to design the controller and establish system stability. To tackle the incommensurate derivatives problem, in each step of the backstepping technique, an appropriate Lyapunov function has been selected based on error variables of the considered step and their boundedness has been proved from the last step to the first one. The computational burden is reduced by decreasing the number of adaptive laws. The developed controller satisfies the output constraints and guarantees convergence of the output tracking error to a small neighborhood of the origin and boundedness of all closed-loop signals. Finally, the effectiveness of the designed controller has been demonstrated via simulating three examples.