Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems With Input and Output Quantization
Xinyi Lu, Fang Wang, Zhi Liu, Ruiyi Zhu, C. L. Philip Chen
Abstract
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, <xref ref-type="lemma" rid="lemma10" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lemmas 10</xref> and <xref ref-type="lemma" rid="lemma11" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</xref> 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.<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i>—In practical remote control systems, because of the limitation of communication channel capacity, signals usually need to be quantized before transmission. However, the most existing fixed-time control schemes for SFNSs do not study the signals quantization. This means that the control processes still rely on the continuous states/output and control input signals, which are not practical in engineering application. Therefore, based on FLSs and command filtering technology, this paper focuses on developing a novel adaptive fuzzy quantized fixed-time control scheme. This scheme ensures that SFNSs under the input and output quantization is still practically fixed-time stable.