Adaptive Fuzzy Fixed-Time Control for Uncertain Non-Linear Systems Based on Complexity Avoidance and a Reduced Order State Observer

The article discusses the fixed-time control trouble of non-linear systems subject to uncertainties and inaccessible states. The uncertainties that appeared in the considered systems will be handled by employing fuzzy logic systems (FLSs). The introduction of the hyperbolic tangent functions effectively avoids the singularity trouble of derivatives of virtual control signals. To solve the computation complexity trouble, the dynamic surface control (DSC) way is employed and a fixed-time hyperbolic tangent filter is used. Specifically, by proving that the reduced order state observers are fixed-time convergent, a fixed-time output-feedback fuzzy control project can be obtained. The stability analysis reveals that the tracking error and observation errors incline to an adjustable interval of zero in the time interval and the boundedness of the states is ensured. Eventually, the examples will be displayed to demonstrate the utilizability of the given way.