Funnel Control of Lower-Triangular Nonlinear Systems With Singular Input-output Links
首发时间:2024-03-15
Abstract:In this article, we delve into the issue of output tracking control with predefined transient behavior for lower-triangular nonlinear systems (LTNSs), especially when faced with the presence of unknown nonlinearities. Unlike the results in the current state of the art, the LTNS under consideration exhibits singular input-output links, which is inherently not feedback linearizable. This general characteristic significantly complicates the controller design process, rendering the tool of adding one power integrator (AOPI) ineffective. In response to this challenge, we develop a novel funnel control (FC) algorithm that ingeniously leverages the bilateral barrier functions (BBFs) alongside the $\varrho-\delta$ definition of limit, to meet predefined transient performance specifications of the output tracking. To validate the efficacy of the proposed FC approach, we conduct a comprehensive evaluation of key performance metrics, including tracking error and transient response.
keywords: Lower-triangular nonlinear systems, output tracking, funnel control, bilateral barrier functions.
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具有奇异输入输出链路的下三角非线性系统漏斗控制
摘要:在本文中, 我们深入研究了对于下三角非线性系统(lower-triangular nonlinear systems, LTNSs)实现具有预设瞬态行为的输出跟踪控制问题, 尤其是存在未知非线性的情况下. 与现有研究成果不同, 所研究的LTNS具有奇异的输入-输出链路, 这从本质上来说是不可反馈线性化的. 这一广义特性显著增加了控制器设计的复杂性, 使得增加幂次积分法(adding one power integrator, AOPI)失效. 为了应对这一挑战, 我们开发了一种新颖的漏斗控制(funnel control, FC)算法, 巧妙地利用双边障碍函数(bilateral barrier functions, BBFs)以及$\varrho-\delta$极限定义, 以满足输出跟踪的预设瞬态性能. 为了验证所提出的FC方法的有效性, 我们对关键性能指标进行了全面评估, 包括跟踪误差和瞬态响应.
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具有奇异输入输出链路的下三角非线性系统漏斗控制
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