Event-triggered Adaptive Neural Control for Pure Feedback Stochastic Nonlinear Systems with Input Saturation and Output State Constraints

This paper proposes a novel event-triggered adaptive neural control scheme for pure-feedback stochastic nonlinear systems subject to input saturation and partial state constraints. By employing the implicit function theorem and mean value theorem, the pure-feedback system is systematically transformed into a strict-feedback form with bounded approximation errors. A key innovation is the introduction of a continuously differentiable asymmetric saturation model based on hyperbolic tangent functions, which accurately characterizes input constraints. The control design integrates backstepping with barrier Lyapunov functions (BLFs) and adaptive neural network, ensuring robust handling of state constraints and stochastic uncertainties at each design step. Theoretical analysis proves that all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB) in probability (fourth-moment sense), while the tracking error converges asymptotically to zero. An event-triggered mechanism further improves computational efficiency. Comparative simulations validate the superiority of the proposed method over conventional approaches.