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Adaptive tracking control for a class of stochastic non‐linear systems with input delay: a novel approach based on multi‐dimensional Taylor network

In this study, by means of the techniques of adaptive multi-dimensional Taylor network (MTN) control, the tracking problem of a class of stochastic non-linear systems with input delay is studied. Firstly, based on the Pade approximation method, a new variable is employed to overcome the problem of input delay, and MTNs are applied to estimate the non-linear functions in the design of the controller. Secondly, an adaptive MTN controller design scheme is developed in the framework of backstepping. Thirdly, the stability of the closed-loop system is analysed using Lyapunov's stability theory. Finally, the effectiveness of the proposed design approach is demonstrated by two examples.