一维布尔格斯方程的采样数据有限维边界控制

Q3 Engineering

IFAC-PapersOnLine Pub Date : 2024-01-01 DOI:10.1016/j.ifacol.2024.10.149

Lina Pan , Pengfei Wang , Emilia Fridman

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引用次数: 0

摘要

在本文中，我们通过模态分解方法和动态扩展，关注在诺伊曼激励下一维布尔格斯方程的区域指数稳定问题。我们考虑了采样数据有限维边界控制，并通过广义保持装置来实现。我们使用基于 Wirtinger 的片断连续时间 Lyapunov 函数来补偿有限维状态的采样，并提供了全阶闭环系统的 H1 稳定性分析。在给定衰减率的情况下，我们提供了高效的线性矩阵不等式（LMI）条件，用于寻找控制器维数和增益，以及吸引力域的约束。我们证明，对于初始值和采样间隔的某些固定上界，LMI 对于某些 N（控制器维数）的可行性意味着它们对于 N + 1 的可行性。数值示例说明了所提方法的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sampled-data finite-dimensional boundary control for 1-D Burgers’ equation

In this paper, we are concerned with the regional exponential stabilization of a 1-D Burgers’ equation under Neumann actuation via modal decomposition method and dynamic extension. We consider a sampled-data finite-dimensional boundary control, which is implemented via a generalized hold device. We use Wirtinger-based piecewise continuous-time Lyapunov functional to compensate sampling of the finite-dimensional state, and provide the H¹-stability analysis for the full-order closed-loop system. Given a decay rate, we provide the efficient linear matrix inequality (LMI) conditions for finding the controller dimension and gain, as well as a bound on the domain of attraction. We prove that for some fixed upper bounds on the initial value and sampling intervals, the feasibility of LMIs for some N (dimension of the controller) implies their feasibility for N + 1. Numerical example illustrates the efficiency of the proposed method.

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来源期刊

IFAC-PapersOnLine Engineering-Control and Systems Engineering

CiteScore

1.70

自引率

0.00%

发文量

1122

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