Output‐feedback adaptive tracking control of stochastic nonlinear systems using multi‐dimensional Taylor network

In this paper, an adaptive multi‐dimensional Taylor network (MTN) control scheme based on the backstepping and dynamic surface control (DSC) is developed to solve the tracking control problem for the stochastic nonlinear system with immeasurable states. The MTNs are used to approximate the unknown nonlinearities, and then based on the multivariable analog of circle criterion, an observer is first introduced to estimate the immeasurable states. By combining the adaptive backstepping technique and the DSC technique, an adaptive MTN output‐feedback backstepping DSC approach is developed. It is shown that the proposed controller ensures that all signals of the closed‐loop system are remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of probability. Finally, the effectiveness of the design approach is illustrated by simulation results.