Abstract

The feedback synthesis problem for a chain of integrators system with continuous bounded unknown perturbation is considered. Our approach is based on the controllability function (CF) method proposed by V.I. Korobov. The perturbation range is determined by the negativity condition for the total derivative of the CF with respect to the perturbed system. The control that does not depend on perturbation under some restrictions and steers an arbitrary initial point from a neighborhood of the origin to the origin in a finite time (settling-time function) is constructed. The settling-time function depends on the perturbation, but it remains bounded from below and from above by the same value.

中文翻译：

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积分系统链反馈综合问题中的摄动范围

摘要

考虑具有连续有界未知扰动的积分系统链的反馈综合问题。我们的方法基于VI Korobov提出的可控制性函数（CF）方法。扰动范围由CF的总导数相对于扰动系统的负性条件确定。构造了在某些限制下不依赖于扰动并在有限时间内将任意初始点从原点附近引导到原点的控制（建立时间函数）。稳定时间函数取决于扰动，但它仍然从下方和上方以相同的值限制。