Geometric, topological, and stochastic approaches in nonlinear control theory

非线性控制理论中的几何、拓扑和随机方法

• 批准号: RGPIN-2016-05405
• 负责人: Mansouri, AbdolReza
• 金额: $ 1.31万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635344
• 关键词: Geometric; topological; stochastic; approaches; nonlinear

Nonlinear control theory is an important branch of control theory, with applications in areas and industries as diverse as power grids, aerospace systems, biomedical systems, nano-engineering, process control, chemical engineering, and many others. It stands out by the richness of its problems and the diversity of mathematical areas that it connects to. Worthy of note among the latter is sub-Riemannian geometry, which continues to play a key role in our understanding of nonlinear control systems. By virtue of restricting itself to a narrow and well-behaved class of control systems, linear control theory enjoys a rich and well-established body of theoretical tools and techniques, drawn principally from linear functional analysis. By contrast, nonlinear control theory is far from enjoying this level of maturity, and intensive efforts have been deployed in devising new tools and approaches.

非线性控制理论是控制理论的一个重要分支，其应用领域和行业广泛，如电网、航空航天系统、生物医学系统、纳米工程、过程控制、化学工程等。它突出了丰富的问题和多样性的数学领域，它连接到。在后者中值得注意的是亚黎曼几何，它继续在我们理解非线性控制系统中发挥关键作用。由于线性控制理论仅限于一类狭窄且性能良好的控制系统，因此它拥有丰富且完善的理论工具和技术，主要来自线性泛函分析。相比之下，非线性控制理论远未达到这种成熟程度，人们已经在设计新的工具和方法方面做出了大量努力。