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Pure Mathematics 2025
分数阶非线性系统的预定时间滑模追踪控制
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Abstract:
本研究旨在设计一种针对高维分数阶非线性系统的滑模追踪控制器，使得系统输出在预定时间内收敛到给定的期望轨迹上。首先，为了便于滑模面的设计，本文利用传统的高阶滑模控制的方法，将复杂系统转化为更为简单的链式系统。然后，将传统的整数阶固定时间滑模控制策略进行改进，设计了两种分数阶滑模面，使其改进的滑模控制方法能够适用于分数阶系统。通过对滑模面的求导和利用Lyapunov稳定性定理，最终所设计的两类分数阶滑模控制器能够使系统的输出在预定时间内追踪上期望轨迹，与传统的固定时间滑模策略相比，该方法可以随意控制系统的最大收敛时间，因而控制效果更优。最后，两个仿真结果证明了这两类控制策略的可行性和有效性。
This research is dedicated to designing a sliding mode tracking controller for high-dimensional fractional-order nonlinear systems, with the objective of making the system output converge to a given desired trajectory within a prescribed-time. In order to facilitate the design of the sliding mode surface, this paper uses the traditional high-order sliding mode control method to transform the complex system into a simpler chained-form system. Subsequently, this paper modifies the traditional integer-order fixed-time sliding-mode control strategy and designs two types of fractional-order sliding mode surfaces, so that the improved sliding-mode control approach can be applied to fractional-order systems. By differentiating the sliding mode surface and leveraging the Lyapunov stability theorem, the two classes of fractional-order sliding mode controllers designed can ensure that the system output tracks the desired trajectory within the prescribed-time. Compared with the traditional fixed-time sliding mode strategy, the proposed method has a significant advantage in that it can freely control the maximum convergence time of the system. Finally, two simulation results demonstrate the feasibility and effectiveness of these two types of control strategies.
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