Predefined-time adaptive fuzzy control of pure-feedback nonlinear systems under input and output quantization

For a class of pure-feedback nonlinear systems, a novel adaptive predefined-time fuzzy control strategy is researched in this paper. Different from the existing nonlinear systems with predefined-time control, both the input and output signals are quantized in this strategy. In the control process, firstly, by utilizing the Butterworth low-pass filter technique to handle the form of pure-feedback and FLSs to approximate the unknown functions, a novel fuzzy state observer is devised to estimate the immeasurable states. Secondly, in the traditional backstepping process, the virtual control signals are usually differentiable. Due to the discontinuity of the output quantization, they are not differentiable which makes the traditional backstepping method not applicable. To handle this issue, a command filtering technique is applied in this strategy. Thirdly, by using a class of smooth functions, an intermediate auxiliary control signal and a novel adaptive predefined-time controller are constructed. Moreover, to compensate the impact of quantization errors, Lemma 9 is proved. On this basis, the proposed strategy can ensure the systems under input and output quantization are practical predefined-time stable. Lastly, an example is applied to demonstrate the feasibility of this strategy.