对于非线性冲动系统的半全球和全球固定时间稳定性
IEEE transactions on cybernetics
|March 3, 2025
概括
本研究引入了分析非线性冲动系统 (NIS) 的新方法,实现半全球和全球固定时间稳定性. 研究为复杂系统提供了新的标准和控制器,确保在有限的时间内保持稳定.
科学领域:
- 控制理论 控制理论
- 非线性动力学是一种非线性动力学.
- 系统工程 系统工程
背景情况:
- 非线性冲动系统 (NIS) 在稳定性分析中存在独特的挑战,原因是冲动引起的集成方法不断变化.
- 现有的方法在全球固定时间稳定性 (GFTS) 的半全球吸引集 (SGAS) 内部和外部与不同的轨迹作斗争.
研究的目的:
- 研究非线性冲动系统 (NIS) 的半全球固定时间稳定性 (SGFTS) 和全球固定时间稳定性 (GFTS).
- 开发理论框架和标准,以在各种冲动条件下实现NIS的固定时间稳定性.
主要方法:
- 动态分区半全球景点集 (SGAS),以解决SGFTS不断发展的整合方法.
- 构建脉冲点的过渡动态,并代计算它们以建立SGFTS条件.
- 引入最大-最小冲动间隔概念,以确保系统进入GFTS的SGAS.
- 在不同脉冲度下制定GFTS的标准,并估计收时间.
主要成果:
- 在NIS的稳定和不稳定冲动下,为SGFTS建立了条件.
- 导出了GFTS的充分条件,确保系统可以从远处进入SGAS.
- 提供了GFTS的标准,具有不同的脉冲度和合时间估计.
- 证明了一种设计的固定时间脉冲控制器的有效性,用于复杂系统的全球稳定.
结论:
- 该研究提供了强大的理论框架,用于分析和实现非线性冲动系统的固定时间稳定性.
- 开发的方法和标准在理解和控制有冲动的复杂动态系统方面取得了重大进展.
- 这些发现对设计能够具有有限时间稳定性的先进控制系统有直接影响.
相关概念视频
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