Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups

IF 1.8 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Mathematics of Control Signals and Systems Pub Date : 2024-07-24 DOI:10.1007/s00498-024-00395-4

Adriano Da Silva, Anderson F. P. Rojas

引用次数: 0

Abstract

In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a compactness assumption on the generalized kernel of the drift. Moreover, this control set is unique and contains the singularities of the drift in its closure.

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零potent 群上线性控制系统非空内部控制集存在的弱条件

在本文中，我们证明了对于零能李群上的线性控制系统，只要对漂移的广义核施加紧凑性假设，李代数秩条件就足以确保存在一个具有非空内部的控制集。此外，这个控制集是唯一的，并且在其闭合中包含漂移的奇点。

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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来源期刊

Mathematics of Control Signals and Systems 工程技术-工程：电子与电气

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematics of Control, Signals, and Systems (MCSS) is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing. Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential equations, differential algebraic equations or difference equations. Potential topics include, but are not limited to controllability, observability, and realization theory, stability theory of nonlinear systems, system identification, mathematical aspects of switched, hybrid, networked, and stochastic systems, and system theoretic aspects of optimal control and other controller design techniques. Application oriented papers are welcome if they contain a significant theoretical contribution.