Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation

In this paper, the problem of adaptive neural tracking control is considered for a class of single-input/single-output (SISO) strict-feedback stochastic nonlinear systems with input saturation. To deal with the non-smooth input saturation nonlinearity, a smooth nonaffine function of the control input signal is used to approximate the input saturation function. Classical adaptive technique and backstepping are used for control synthesis. Based on the mean-value theorem, a novel adaptive neural control scheme is systematically derived without requiring the prior knowledge of bound of input saturation. It is shown that under the action of the proposed adaptive controller all the signals of the closed-loop system remain bounded in probability and the tracking error converges to a small neighborhood around the origin in the sense of mean quartic value. Two simulation examples are provided to demonstrate the effectiveness of the presented results.