In this article, a novel second order sliding mode control strategy is proposed for relative-degree-2 nonlinear uncertain single- input-single-output (SISO) systems. To design the strategy, the phase portrait of the second order system in normal form associated with the formulated sliding mode control problem is studied. A sliding surface switching between arcs of parabolas is conceived to ensure the convergence in a predefined-time to the desired second order sliding mode. Lyapunov-based analysis and the reformulation of LaSalle-Yoshizawa results for nonsmooth systems are used to prove the uniform finite-time stability of the equilibrium consisting in the second order sliding mode enforcement. This in turn allows to prove the asymptotic convergence of the original plant state to the origin in spite of the uncertainties.

中文翻译：

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通过二阶滑模生成实现预定义时间输出稳定


在本文中，针对相对度2非线性不确定单输入单输出（SISO）系统提出了一种新颖的二阶滑模控制策略。为了设计该策略，研究了与公式化滑模控制问题相关的正规形式的二阶系统的相图。设想在抛物线弧之间切换滑动表面以确保在预定时间内收敛到所需的二阶滑动模式。基于李亚普诺夫的分析和非光滑系统的拉萨尔-吉泽结果的重新表述被用来证明二阶滑模执行中平衡的一致有限时间稳定性。尽管存在不确定性，这反过来又可以证明原始植物状态与原点的渐近收敛性。