The issue of fast finite-time adaptive control is studied for quantized stochastic nonlinear systems. Unlike the existing works about fast finite-time control, the input signals are quantized, and the stochastic disturbances and nonlinear functions are unknown. According to universal approximation capacity of fuzzy logic system, combined with backstepping technique, a novel fast finite-time adaptive fuzzy control strategy of quantized stochastic nonlinear system is proposed. The nonlinear decomposition method is introduced to set up the relationship among the control signals and the quantization signals, which overcomes the technical difficulties result from the piecewise quantization input. The proposed tactics can assure the tracking error situate in a neighborhood of the origin point and the closed-loop system signals keep bounded. Finally, an algorithm simulation is conducted to test the validity of the method.

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This paper concentrates upon the issue of adaptive fuzzy tracing control for a class of nonstrict‐feedback nonlinear systems output with hysteresis via an event‐triggered strategy. To handle the difficulty caused by the nonstrict nonlinear systems, the variable separation technique is introduced. The design difficulty of output hysteresis is addressed by employing a hysteresis inverse function and Nussbaum function to compensate unmeasurable state signal. Meanwhile, the fuzzy logic system (FLS) is used to estimate the unknown function at each step of recursion. Moreover, by devising the relative threshold event‐triggered mechanism (ETM), the frequency of actuators and controllers can be largely decreased. Thus, the adaptive fuzzy event‐triggered tracing control strategy is proposed by combining the barrier Lyapunov function and backstepping technique. With the proposed scheme, it is theoretically demonstrated that all signals in the closed‐loop system are bounded, and the tracing errors are driven to a small neighborhood of the origin under the output constraint. Eventually, two examples demonstrate the efficacy of the proposed control strategy.