CAREER: Multiscale Control of Mechanical Systems: Theory, Computation and Applications

职业：机械系统的多尺度控制：理论、计算和应用

• 批准号: 1847802
• 负责人: Molei Tao
• 金额: $ 40.03万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1847802&HistoricalAwards=false
• 关键词: CAREER; Multiscale; Control; Mechanical; Systems

This project seeks to develop a new area termed multiscale control. Such a development will increase our ability to control practical systems. Due to physical and technological limitations, available ways of perturbing a mechanical system are often constrained. For example, it is difficult to individually force single atoms in order to control a molecular system. On the other hand, partial intervention is often easier; for instance, an oscillatory electromagnetic field can interact with charged atoms and induce perturbations to the system, which are however in restricted forms. When the available perturbations are restricted, they may be inadequate to induce immediate favorable changes to the system. However, the key idea is that, if introduced at a smaller scale, perturbations can accumulate and contribute in less restrictive ways to the original scale. Based on this idea, the project develops a framework for designing the perturbation so that its accumulated effect can alter the system's macroscopic behavior in a desired fashion. Numerical computations and the development of computational tools will also be seamlessly integrated with the theoretical analysis. To illustrate the innovation of the proposed research, note that traditional control theory is still important, albeit insufficient, because the control is introduced at a microscopic level, yet one needs and only needs to control the system's macroscopic behavior. Brute-force computational search for the optimal control will also be practically infeasible due to the wide breadth of scales presented in the system. The research is to use theoretical analysis (based on tools from fields such as dynamical systems and multiscale methods) to either directly design or accelerate the computational search of control strategies. The study will also be complemented by investigations in multiple interdisciplinary applications, such as DNA deactivation, remote control of locomotion, temporal metamaterials, and recovery of material defects. Research will be integrated with education across multiple institutions and over the spectrum of academic levels. Specifics are planned for broadening women and underrepresented groups' participation and disseminating knowledge beyond PI's immediate institute or discipline.More specifically, this project identifies (mostly-)oscillatory perturbations for accomplishing various control tasks, such as to steer a system from a macroscopic state to another, or to track a desired dynamic behavior at the macroscopic level for all time. The main methodology is to design microscopic perturbations that resonantly interact with the system, so that nontrivial effects cascade to the macroscopic scale. The PI has already obtained several preliminary results on this idea, and the proposed theory will be a generalization. The strategy of investigation is to first quantify how small-scale perturbations effectively accumulate at large-scale using dynamical systems tools, asymptotic/multiscale methods, and numerical computations, followed by the patching together of the local understandings for the global objective of control design. An example of core tasks is to identify and then track slowly-varying resonant frequencies in nonlinear systems. Integrable, nearly-integrable, and stochastic systems will be considered, so that an ambitious goal of controlling complicated dynamics can be gradually approached.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目旨在开发一个称为多尺度控制的新领域。这种发展将提高我们控制实际系统的能力。由于物理和技术的限制，扰动机械系统的可用方法通常受到限制。例如，很难单独地迫使单个原子来控制分子系统。另一方面，部分干预通常更容易;例如，振荡电磁场可以与带电原子相互作用，并对系统产生扰动，但这些扰动的形式受到限制。当可用的扰动受到限制时，它们可能不足以引起系统的立即有利变化。然而，关键的想法是，如果在较小的尺度上引入，扰动可以积累并以较少限制的方式对原始尺度做出贡献。基于这一想法，该项目开发了一个框架，用于设计扰动，使其累积效应可以以所需的方式改变系统的宏观行为。数值计算和计算工具的开发也将与理论分析无缝集成。为了说明所提出的研究的创新，请注意，传统的控制理论仍然是重要的，虽然不够，因为控制是在微观层面上引入的，但人们需要而且只需要控制系统的宏观行为。暴力计算搜索的最佳控制也将是实际上不可行的，由于广泛的范围内提出的系统。该研究将使用理论分析（基于动力系统和多尺度方法等领域的工具）来直接设计或加速控制策略的计算搜索。该研究还将通过多个跨学科应用的研究来补充，例如DNA失活，运动的远程控制，时间超材料和材料缺陷的恢复。研究将与跨多个机构和学术水平的教育相结合。具体计划是扩大妇女和代表性不足的群体的参与和传播PI的直接研究所或学科以外的知识。更具体地说，该项目确定（主要是）振荡扰动完成各种控制任务，如从一个宏观状态转向另一个系统，或跟踪一个期望的动态行为在宏观水平的所有时间。主要的方法是设计与系统共振相互作用的微观扰动，使非平凡的影响级联到宏观尺度。PI已经获得了一些关于这个想法的初步结果，所提出的理论将是一个推广。调查的策略是首先量化小规模扰动如何有效地积累在大规模使用动力系统工具，渐近/多尺度方法，和数值计算，其次是修补在一起的局部理解的控制设计的全球目标。核心任务的一个例子是识别并跟踪非线性系统中缓慢变化的谐振频率。可积、近可积和随机系统将被考虑，以便控制复杂动力学的宏伟目标可以逐步实现。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

A Derivative-Free Optimization Method With Application to Functions With Exploding and Vanishing Gradients

• DOI: 10.1109/lcsys.2020.3004747
• 发表时间: 2021-04-01
• 期刊: IEEE CONTROL SYSTEMS LETTERS
• 影响因子: 3
• 作者: Al-Abri, Said;Lin, Tony X.;Zhang, Fumin
• 通讯作者: Zhang, Fumin

Generation of Electromechanical Frequency Combs in Fluid Media with a Parametrically Driven Capacitive Microresonator

使用参数驱动电容微谐振器在流体介质中生成机电频率梳

• DOI: 10.1103/physrevapplied.19.044021
• 发表时间: 2023
• 期刊: Physical Review Applied
• 影响因子: 4.6
• 作者: Surappa, Sushruta;Wei, Charles;Tao, Molei;Degertekin, F. Levent
• 通讯作者: Degertekin, F. Levent

Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian

• DOI: 10.48550/arxiv.2210.00090
• 发表时间: 2022-09
• 期刊: ArXiv
• 作者: Oswin So;Gongjie Li;Evangelos A. Theodorou;Molei Tao

Dynamic mode decomposition for multiscale nonlinear physics

• DOI: 10.1103/physreve.99.063311
• 发表时间: 2019-06-20
• 期刊: PHYSICAL REVIEW E
• 影响因子: 2.4
• 作者: Dylewsky, Daniel;Tao, Molei;Kutz, J. Nathan
• 通讯作者: Kutz, J. Nathan

AhKin: A modular and efficient code for the Doppler shift attenuation method

AhKin：多普勒频移衰减方法的模块化高效代码

• DOI: 10.1016/j.cpc.2019.07.017
• 发表时间: 2020
• 期刊: Computer Physics Communications
• 影响因子: 6.3
• 作者: Garzón, Alejandro;Rodriguez, Wilmar;Cristancho, Fernando;Tao, Molei
• 通讯作者: Tao, Molei