Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems With Input and Output Quantization

The most existing studies on fixed-time control are restricted to nonlinear systems without the quantized signals. To remove this restriction, for a class of strict-feedback nonlinear systems (SFNSs) with input and output quantization, a new adaptive fuzzy fixed-time control scheme is presented in this article. Firstly, since the functions in SFNSs are unknown, fuzzy logic systems (FLSs) are applied to approximate them. Based on the quantized input and output signals, a novel fuzzy state observer is devised to evaluate the unmeasurable states. Secondly, in the backstepping design process, because of the discontinuity of output quantization, the partial derivatives of the virtual control signals are difficult to obtain. To get over this difficulty, a command filtering technology is adopted. Furthermore, an actual quantized fixed-time controller and novel parameter adaptive laws are established. Thirdly, to compensate the effects of the quantization errors, Lemmas 10 and 11 are presented. It is indicated that the presented control scheme can ensure the practical fixed-time stability of control systems. Finally, an example is given to demonstrate the effectiveness of the presented scheme.