Composite adaptive fuzzy backstepping control of uncertain fractional-order nonlinear systems with quantized input

This paper studies the adaptive fuzzy backstepping control of strict-feedback fractional-order nonlinear systems subject to quantized input with known and unknown quantization parameters. A command filter is designed to finish off the “explosion of complexity” issue caused by differentiating virtual control inputs repeatedly in each backstepping step, and a compensated signal is implemented to reduce the negative impact of filtered errors. In addition, the prediction error calculated by a fractional-order serial-parallel model is combined into the fuzzy adaptation law so that functional uncertainties can be accurately approximated by fuzzy logic systems. Importantly, the control input is forced to pass through a hyperbolic tangent function, and a parameter identifier is developed to identify unknown quantization parameters, which can achieve the purpose of compensating quantization errors. The final quantized input signal can ensure that tracking errors converge to a small region, and all the signals involved keep semi-globally uniformly bounded based on the fractional Lyapunov stability criterion. Finally, the availability of the used method is testified through two simulation experiments.