The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
基本信息
- 批准号:RGPIN-2019-04554
- 负责人:
- 金额:$ 1.53万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2019
- 资助国家:加拿大
- 起止时间:2019-01-01 至 2020-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research is connected with the area of control theory, a field with many areas of application, ranging from robotics, to chemical processes, to scheduling of medical treatments. The primary focus of the work is on a sub-discipline of control theory known as geometric control theory. The tools of geometric control theory are most useful for studying control systems described by ordinary differential equation models that are not linear. For nonlinear ordinary differential equation models, many of the basic problems of control theory remain unanswered. Three such important basic problems are (1) controllability, (2) stabilisability, and (3) optimality. The problem of controllability is, in rough terms, that of using control to steer a system from a given initial state to a desired final state. A simple example is the steering of a mobile robot from one configuration to another. The problem of stabilisability is to use control to render a (possibly unstable) behaviour stable. A simple example is the balancing of a pendulum in its upright configuration. The problem of optimality is that of determining whether a given behaviour minimises a prescribed cost. A simple example is the mobile robot steering problem mentioned above, but now requiring that the reconfiguration be done while using the least possible energy.******All three of these problems have a component of their resolution that relies on a detailed understanding of the local structure of a system. It is the aim of this work to understand this local structure with the objective of coming to a more complete understanding of the basic problems described above. While existing work has contributed greatly to our understanding of this structure, it is fair to say that a comprehensive understanding remains elusive. To make advances on this understanding, the proposed research uses a new modelling framework for geometric control systems, one founded in the mathematics of advanced functional analysis, sheaf theory, and pseudogroups. Functional analysis is used to topologise spaces of vector fields, and recent work by the proposer's group has made significant advances by understanding this topology for real analytic vector fields, an especially important case for geometric control theory. With these functional analysis tools, it becomes possible to employ methods of sheaf theory (for spaces of vector fields) and the theory of pseudogroups (for spaces of flows) to express the subtle behaviour exhibited by control systems. These tools have hitherto not been widely used in control theory, and so provide unexplored avenues for fruitful future work.******The proposal is concerned with a long-term program of basic research. The intention of the work, however, is to shed light on applied problems, and eventually produce methodologies based on the deep understanding revealed by new results and techniques. An important facet of the proposal is to utilise and train highly qualified personnel.
这项研究与控制理论领域相关,该领域有许多应用领域,从机器人技术到化学过程,再到医疗安排。 这项工作的主要重点是控制理论的一个子学科,即几何控制理论。 几何控制理论的工具对于研究由非线性常微分方程模型描述的控制系统最有用。 对于非线性常微分方程模型,控制理论的许多基本问题仍未得到解答。 三个重要的基本问题是(1)可控性、(2)稳定性和(3)最优性。 粗略地说,可控性问题是使用控制来引导系统从给定的初始状态到所需的最终状态。 一个简单的例子是移动机器人从一种配置转向另一种配置。 稳定性问题是使用控制来使(可能不稳定的)行为稳定。 一个简单的例子是垂直配置的摆的平衡。 最优性问题是确定给定行为是否最小化规定成本。 一个简单的例子是上面提到的移动机器人转向问题,但现在要求在使用尽可能少的能量的情况下完成重新配置。******所有这三个问题的解决方案都有一个依赖于详细理解的组成部分系统的局部结构。 这项工作的目的是了解这种局部结构,以便更全面地理解上述基本问题。 虽然现有的工作极大地促进了我们对这种结构的理解,但公平地说,全面的理解仍然难以实现。 为了推进这一理解,本研究采用了一种新的几何控制系统建模框架,该框架建立在高级泛函分析、层理论和伪群的数学基础上。 泛函分析用于拓扑向量场空间,提出者小组最近的工作通过理解实解析向量场的拓扑取得了重大进展,这对于几何控制理论来说是一个特别重要的案例。 有了这些泛函分析工具,就可以采用层理论(对于矢量场空间)和伪群理论(对于流空间)来表达控制系统所表现出的微妙行为。 迄今为止,这些工具尚未在控制理论中得到广泛应用,因此为未来富有成效的工作提供了尚未探索的途径。******该提案涉及一项长期的基础研究计划。 然而,这项工作的目的是阐明应用问题,并最终根据新结果和技术所揭示的深刻理解产生方法论。 该提案的一个重要方面是利用和培训高素质人才。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Lewis, Andrew其他文献
Pilot Study Comparing Systemic and Tissue Pharmacokinetics of Irinotecan and Metabolites after Hepatic Drug-Eluting Chemoembolization.
比较肝脏药物洗脱化疗栓塞后伊立替康和代谢物的全身和组织药代动力学的初步研究。
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:0
- 作者:
Levy, Elliot B;Peer, Cody;Sissung, Tristan M;Venkatesan, Aradhana;Pandalai, Prakash;Greten, Tim;Hughes, Marybeth S;Garcia, Charisse;Peretti, Julie;Figg, William;Lewis, Andrew;Wood, Bradford - 通讯作者:
Wood, Bradford
Concise Review: Regulation of Self-Renewal in Normal and Malignant Hematopoietic Stem Cells by Krüppel-Like Factor 4.
简评:Krüppel 样因子 4 对正常和恶性造血干细胞自我更新的调节。
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:6
- 作者:
Park, Chun S;Lewis, Andrew;Chen, Taylor;Lacorazza, Daniel - 通讯作者:
Lacorazza, Daniel
Structure-activity-relationship studies of conformationally restricted analogs of combretastatin A-4 derived from SU5416.
来自 SU5416 的考布他汀 A-4 构象限制类似物的结构-活性-关系研究。
- DOI:
- 发表时间:
2006-10-01 - 期刊:
- 影响因子:3.5
- 作者:
Pandit, Bulbul;Sun, Yanjun;Chen, Ping;Sackett, Dan L;Hu, Zhigen;Rich, Wendy;Li, Chenglong;Lewis, Andrew;Schaefer, Kevin;Li, Pui - 通讯作者:
Li, Pui
Acidic environments trigger intracellular H+-sensing FAK proteins to re-balance sarcolemmal acid-base transporters and auto-regulate cardiomyocyte pH.
酸性环境触发细胞内 H 感应 FAK 蛋白,重新平衡肌膜酸碱转运蛋白并自动调节心肌细胞 pH 值。
- DOI:
- 发表时间:
2022-11-10 - 期刊:
- 影响因子:10.8
- 作者:
Wilson, Abigail D;Richards, Mark A;Curtis, M Kate;Gunadasa;Monterisi, Stefania;Loonat, Aminah A;Miller, Jack J;Ball, Vicky;Lewis, Andrew;Tyler, Damian J;Moshnikova, Anna;Andreev, Oleg A;Reshetnyak, Yana K;Carr, Carolyn;Swietach - 通讯作者:
Swietach
Decreasing the flexibility of the TELSAM-target protein linker and omitting the cleavable fusion tag improves crystal order and diffraction limits.
降低 TELSAM 目标蛋白接头的灵活性并省略可切割的融合标签可改善晶体顺序和衍射极限。
- DOI:
- 发表时间:
2023-05-15 - 期刊:
- 影响因子:0
- 作者:
Gajjar, Parag L;Romo, Maria J Pedroza;Litchfield, Celeste M;Callahan, Miles;Redd, Nathan;Nawarathnage, Supeshala;Soleimani, Sara;Averett, Jacob;Wilson, Elijah;Lewis, Andrew;Stewart, Cameron;Tseng, Yi;Doukov, Tzanko;Lebedev, Andrey;Mood - 通讯作者:
Mood
Lewis, Andrew的其他文献
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{{ truncateString('Lewis, Andrew', 18)}}的其他基金
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2022
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2022
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2021
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2021
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2020
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2020
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
On the interplay of controllability and stabilisation
关于可控性和稳定性的相互作用
- 批准号:
217005-2013 - 财政年份:2017
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
On the interplay of controllability and stabilisation
关于可控性和稳定性的相互作用
- 批准号:
217005-2013 - 财政年份:2017
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
On the interplay of controllability and stabilisation
关于可控性和稳定性的相互作用
- 批准号:
217005-2013 - 财政年份:2015
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
On the interplay of controllability and stabilisation
关于可控性和稳定性的相互作用
- 批准号:
217005-2013 - 财政年份:2015
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
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相似海外基金
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2022
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2022
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2021
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2021
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
The exponential map for flows and its application in geometric control theory
流动指数图及其在几何控制理论中的应用
- 批准号:
RGPIN-2019-04554 - 财政年份:2020
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual