For stochastic nonlinear systems with time-delay, most of the existing control approaches with infinite-time stabilization fail to achieve a rapid response from transient state to steady state as they tend to be too conservative. Here, the issue of finite-time adaptive control based on the multi-dimensional Taylor network (MTN) for a class of stochastic nonlinear time-delay systems with dead zone is investigated. The effect of time delay is compensated by designing a suitable Lyapunov-Krasovskii functional (LKF). And the finite-time control method is introduced to secure fast transient performance. A characteristic function is constructed to eliminate the influence of the dead zone. Moreover, in the process of the controller design, unknown nonlinear functions can be approximated using MTN. Based on the finite-time control approach and Lyapunov stability theory, a finite-time adaptive MTN control scheme is proposed to ensure that all the closed-loop signals are semi-global finite-time stable in probability (SGFTSP), and the tracking error converges to a small neighborhood of the origin in finite-time. Two simulation examples are provided to verify the effectiveness of the presented controller.
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