Adaptive multi‐dimensional Taylor network tracking control for SISO uncertain stochastic non‐linear systems

Abstract

In this study, the problem of adaptive multi-dimensional Taylor network (MTN) control for single-input single-output (SISO) uncertain stochastic non-linear systems is investigated. How to minimise the influence of randomness and uncertain non-linearity for less complex computation, and how to improve the real-time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non-linear systems. MTNs are used to approximate the non-linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real-time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real-time performance and control quality.