Prescribed tracking of stochastic nonlinear systems with indifferentiable non-affine terms and dead zone

Abstract

This paper considers the constrained tracking problem for a class of stochastic nonlinear systems with non-affine terms and dead zone. The non-affine terms are not required to be differentiable, resulting in that the traditional algorithms cannot address the tracking problem efficiently. To this end, a semi-bounded condition is utilized to convert the non-affine terms into a pseudo-affine form. Moreover, the transformed systems include extra undesired spilled variables and the asymmetric dead zone input. The separation and approximation technique of neural networks are used to address this issue. By introducing a performance function, an adaptive controller is developed such that the signals of the closed-loop system are bounded in probability, and the tracking error satisfies the prescribed performance. Simulation results demonstrate the effectiveness of the proposed method.