Neural-network-based adaptive tracking control for a class of pure-feedback stochastic nonlinear systems with backlash-like hysteresis

In this paper, we are concerned with the problem of adaptive neural network tracking control for a class of pure-feedback stochastic nonlinear systems with backlash-like hysteresis. Unlike some existing control schemes, an affine variable at each step is constructed without using the mean value theorem, and neural networks are used to approximate the unknown and desired control input signals. By introducing the additional first-order low-pass filter for the actual control input signal, the algebraic loop problem arising in pure-feedback stochastic nonlinear systems with backlash-like hysteresis is addressed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability while the tracking error converges to a small neighborhood of the origin in the sense of four-moment. Finally, a simulation example is given to verify the effectiveness of the proposed scheme.