Controllability of periodic linear systems, the Poincaré sphere, and quasi-affine systems

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

Mathematics of Control Signals and Systems Pub Date : 2023-10-04 DOI:10.1007/s00498-023-00369-y

Fritz Colonius, Alexandre Santana, Juliana Setti

引用次数: 0

Abstract

Abstract For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here, a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere, one obtains a compactification of the state space allowing us to describe the behavior “near infinity” of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior.

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周期线性系统的可控性，庞卡罗球，和准仿射系统

摘要对于控制范围有界的周期线性控制系统，通过在系统状态中加入相位，引入了一个自治系统。这里存在一个唯一的控制集(即近似可控性的极大集)，其内部是非空的。它是由齐次部分的谱子空间决定的，齐次部分是一个周期线性微分方程。利用庞加莱球，我们得到了状态空间的紧化，使我们能够描述原始控制系统的“近无穷”行为。进一步，将其应用于拟仿射系统，得到了具有非空内部的唯一控制集。

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.