Adaptive neural control for stochastic pure‐feedback non‐linear time‐delay systems with output constraint and asymmetric input saturation

In this study, the adaptive tracking control is investigated for a class of stochastic pure-feedback non-linear time-delay systems with output constraint and asymmetric input saturation non-linearity. First, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation model, and the barrier Lyapunov function is designed to cope with the output constraints. Then, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to address the effects of the unknown time-delay terms, and the neural network is employed to approximate the unknown non-linearities. At last, based on Lyapunov stability theory, a robust adaptive neural controller is proposed, which decreases the number of learning parameters and thus avoids the over-estimation problem. Under the designed neural controller, all the closed-loop signals are guaranteed to be 4-moment (or 2 moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighbourhood of the origin for bounded initial conditions. Two simulation examples are presented to further illustrate the effectiveness of the designed method.