This paper presents a predefined-time control of fractional-order linear system subject to a large class of continuous but not necessarily integer-order differentiable disturbances. The dynamical system is based on the Caputo derivative and has an order that lies in (1,2). The proposed controller, based on a dynamic extension, induces an integer-order reaching phase, such that an invariant second-order sliding mode is enforced in predefined-time, that is, the solution of the fractional-order system and its integer-order derivative converge to the origin within a time that is prescribed as a tunable control parameter. The controller is continuous and able to compensate for unknown continuous disturbances. A simulation study is carried out in order to show the effectiveness of the proposed scheme.

中文翻译：

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分数阶系统的二阶预定义时间滑模控制

本文提出了一种分数阶线性系统的预定义时间控制，该系统受到大量连续但不一定是整数阶可微扰动的影响。动力系统基于 Caputo 导数，阶数位于 (1,2) 中。所提出的控制器基于动态扩展，引入整数阶到达阶段，从而在预定义的时间内强制执行不变的二阶滑模，即分数阶系统及其整数阶的解导数在规定为可调控制参数的时间内收敛到原点。控制器是连续的并且能够补偿未知的连续干扰。为了证明所提出方案的有效性，进行了仿真研究。