Design, analysis, and application of fixed-time convergence fuzzy ZNN model realized by dynamic fuzzy logic system for time-varying Sylvester equation

Due to the strengths of zeroing neural network (ZNN) in dealing with time-varying problems and the advantages of fuzzy logic system (FLS) in uncertain computing, a fixed-time convergence fuzzy ZNN (FTCFZNN) model realized by the FLS with dynamic membership functions is proposed for solving time-varying Sylvester equation (TVSE). The introduction of the dynamic membership functions in the FLS is one of the most meaningful attributes of this paper, and such a FLS is called the dynamic FLS (DFLS). The design parameter of the FTCFZNN model is the fuzzy parameter generated by the DFLS. Meanwhile, the fuzzy parameter is also employed in the proposed adaptive activation function, which makes the FTCFZNN model possess fixed-time convergence with less upper bound and has a better adaptable ability. Moreover, a series of theoretical analyses reflect the superior fixed-time convergence and adaptive robustness of the FTCFZNN model. Numerical simulations demonstrate the predominant performance of the FTCFZNN model and its effectiveness in solving the TVSE compared with serval existing ZNN models. Finally, the FTCFZNN model is applied to realize the consensus of multi-agent systems, which shows the application value of the FTCFZNN model.