Adaptive Control for Stochastic Nonlinear Systems with Input Saturation Based on Multi-dimensional Taylor Network

For stochastic nonlinear systems with input saturation, few of the existing control methods use a suitable auxiliary system to solve input saturation problem, and most of them are for deterministic systems. In this study, according to the backstepping approach and the Lyapunov stability theorem, utilizing multi-dimensional Taylor network (MTN), an adaptive controller is presented to secure that all closed-loop signals keep bounded in probability, in which MTN is implemented to approach the uncertain function during the controller design. Moreover, the impact raised by input saturation is mitigated by designing an appropriate auxiliary system, in which the order of the auxiliary system is the same as that of the controlled system. Furthermore, unlike the majority of prior findings, the final output signal could be constrained in a mean quartic sense by an explicit expression of the input saturation error (the difference between the control signal and the saturation input) and the parameters used for design. Finally, the efficiency of the suggested control methodology is confirmed by providing an example.