Observer-Based Adaptive Fuzzy Output Feedback Control of Fractional-Order Chaotic Systems With Input Quantization

Abstract

This study investigates the adaptive fuzzy output feedback control of strict-feedback fractional-order chaotic systems with unmeasurable states and quantized input. First, the functional uncertainties are approximated by fuzzy logic systems (FLSs). Second, combining the FLS and the system output signal, an observer is constructed to estimate the unmeasurable states. A command filter is defined to cope with the “explosion of complexity” problem resulting from the repeated derivatives of virtual control inputs in each backstepping step. To compensate for quantization errors, a hyperbolic tangent function is introduced to transform the control signal, which can not only guarantee that the tracking error converges to an arbitrarily small region near the origin but also reduce the chattering phenomenon of the control input. In addition, the stability analysis is carried out relying on the fractional Lyapunov stability criterion such that all the signals keep bounded. Finally, a numerical simulation example is put forward to verify the effectiveness of our method.