CAREER: Towards Scale-Invariant Identification and Synthesis Algorithms for Control Using Randomization

智能城市基础设施和互联网等网络系统是工程学的胜利。然而，为这种规模的系统建模和设计控制器在技术上和计算上都是具有挑战性的，在最坏的情况下是难以处理的。随着这些和未来系统的规模、复杂性和连接性的加速，技术挑战也在增加。反馈控制是一种机制，使工程师能够保证理想的系统行为，如稳定性（干扰的影响是否随着时间的推移而衰减？）、性能（系统是否有效运行？）和鲁棒性（尽管在不确定的环境中运行，性能和稳定性能否保持？）。对于网络系统，反馈控制只能以分布式的方式应用，没有中央决策者。不幸的是，分布式控制在理论上和计算上都比集中式控制更具挑战性。此外，分布式控制需要通过网络传输潜在的敏感数据。尽管最近在分布式控制和数据隐私方面取得了进展，但我们可以控制的系统的复杂性与我们想要控制的系统的复杂性之间存在很大差距。当我们额外要求数据隐私保证时，差异会进一步增加。该项目旨在弥合理论、可扩展计算和数据隐私之间的差距，从而帮助我们建立安全可靠的自主系统。这项研究的结果将使分布式控制在航空航天、机器人、汽车和能源行业的广泛采用成为可能。本项目包括三个基础研究课题；I)从部分观测数据中学习动态系统模型，ii)从模型中设计鲁棒和最优的分布式控制器，以及iii)将数据隐私机制集成到建模和控制工作流中。本研究项目的争论点在于，使用传统的“精确”方法是不可能实现大规模网络系统的这些目标的。相反，我们将制定学习和控制问题的“近似值”，这些问题可以以解决完整问题的一小部分成本来解决。如果设计正确，这些近似可以为原大型系统提供稳定性和性能保证。为了实现这个公式，我们将基于数值线性代数和高维概率的随机化方法开发新的理论和算法，为分布式控制问题定制。此外，随着敏感数据在近似阶段被压缩和转换，数据隐私自然会被考虑在内。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Networked systems such as smart city infrastructure and the Internet are engineering triumphs. However, modeling and designing controllers for systems of this scale is technically and computationally challenging at best, and intractable in the worst case. As the magnitude, complexity, and connectivity of these and future systems accelerates, so too do the technical challenges. Feedback control is the mechanism that enables engineers to guarantee desirable system behaviors such as stability (do the effects of disturbances decay over time?), performance (is the system operating efficiently?), and robustness (can performance and stability be maintained despite operating in an uncertain environment?). For networked systems, feedback control can only be applied in a distributed manner, there is no central decision maker. Unfortunately, distributed control is theoretically and computationally more challenging than its centralized counterpart. Moreover, distributed control requires transmission of potentially sensitive data over a network. Despite recent progress in distributed control and data privacy, there is a large gap between the complexity of systems we can control, and complexity of systems we want to control. The difference further increases when we additionally ask for data privacy guarantees. This project seeks to bridge the gap between theory, scalable computation, and data privacy and thus help make autonomous systems that we depend upon safe and trustworthy. Results from this research will enable the widespread adoption of distributed control in the aerospace, robotics, automotive, and energy industries.This project consists of three foundational research topics; i) learning a dynamical system model from partially observed data, ii) designing robust and optimal distributed controllers from the model, and iii) integrating data privacy mechanisms into the modeling and control workflow. The contention of this research project is that it is impossible to achieve these goals for large-scale networked systems using traditional “exact” methods. Instead we will formulate “approximations” of the learning and control problems that can be solved at a fraction of the cost of doing so for the full problem. Correctly designed, these approximations can provide stability and performance guarantees for the original large-scale system. To achieve this formulation, we will develop new theory and algorithms based on randomized methods for numerical linear algebra and high-dimensional probability, customized for distributed control problems. Moreover, data privacy will be naturally accounted for as sensitive data gets compressed and transformed in the approximation stages.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.