Fractional order adaptive backstepping output feedback control: The incommensurate case

This paper investigates the problem pertained to adaptive backstepping control for a class of incommensurate fractional order nonlinear systems. The controlled plant is of parametric strict-feedback form with unknown parameters, varying disturbance and partial measurable state. To solve this problem, a novel state observer is constructed first and then an adaptive control law is developed via the backstepping procedure. The required fractional order derivatives of some given signals are generated by our fractional order tracking differentiator in real time. The asymptotic stability of the closed-loop control system is proven in virtue of indirect Lyapunov method. Finally, the efficiency and applicability of our theoretical results are validated by one illustrate example.