CAREER: A Unified Theory of Private Control Systems

职业：私人控制系统的统一理论

• 批准号: 2422260
• 负责人: Matthew Hale
• 金额: $ 50万
• 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: 2024
• 资助国家: 美国
• 起止时间: 2024-03-01 至 2025-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2422260&HistoricalAwards=false
• 关键词: CAREER; Unified; Theory; Private; Control

The recent advances in artificial intelligence and wireless sensor technologies have led to significant research in cooperative optimization. In this regime, multiple agents (e.g., processors or sensors) communicate their information locally with their neighbors to cooperatively optimize a global performance metric. This decentralized paradigm plays a key role in the network domains where communication with a centralized coordinator is either undesirable or impossible. This also allows for preserving the privacy of the agents. It is for these reasons that the design and performance analysis of decentralized optimization methods have attracted a growing attention in several application domains such as data science, wireless networks, and communication networks. This project is aimed at development of new models, mathematical tools, and computational algorithms to address emerging complex multi-agent systems. This complexity arises in emerging applications such as remote sensing, economic dispatch models with renewable energy, and efficiency estimation in transportation networks. This proposal has the potential to substantially reduce the gap between the theory and real-world practice of complex multi-agent networks. Moreover, collaborations with the industrial partner will facilitate effective knowledge transfer. This project is also aimed at increasing awareness and interest among high school students, educators, and college students through several fully integrated educational and outreach activities. These include enhancing professional development of teachers of Stillwater High School, engaging secondary students in after school activities, and promoting diversity through involvement of underrepresented undergraduate students in research. The long-term research goal is to advance the computational models and algorithms for distributed constrained optimization in emerging complex multi-agent networks. In pursuit of this goal, the research objective of this CAREER proposal is to apply the theory of variational inequalities and regularization in the field of distributed optimization to design new algorithms with provable performance guarantees that can address multi-agent networks with complex constraints. This complexity arises in several application domains such as wireless sensor networks, transportation networks, and machine learning, where the optimization model is complicated due to the presence of: (1) uncertainty and nonlinearity in constraints; (2) an inner-level large-scale optimization problem; or (3) equilibrium constraints. The state-of-the-art approaches including weighted-averaging consensus, push-sum, and alternate direction multiplier methods work often under the premise that functional constraints are easy-to-project. These schemes rely significantly on Lagrangian duality theory and do not lend themselves to asynchronous protocols and communication delays. Accordingly, this research is expected to advance the area of distributed optimization over complex networks by: (i) Development of an enhanced mathematical modeling framework by utilizing the theory of variational inequalities; (ii) Design and analysis of new classes of iteratively regularized consensus-based algorithms with explicit performance bounds to address the proposed modeling framework; and (iii) Explore novel ways to address nonsmoothness in the proposed modeling framework. The long-term educational goal is to broaden the participation of K-12 and college students (in particular women and underrepresented minorities in STEM) in the fields of Operations Research and Applied Mathematics. In pursuit of this goal, the educational objective of this CAREER proposal is to inspire and engage young minds, formal and informal educators, and undergraduate and graduate students in understanding the role of optimization in tomorrow’s practice. This includes the following activities: (i) provide four-week professional development workshops for secondary teachers; (ii) develop an after school STEM program for Stillwater High School students; (iii) involve underrepresented undergraduate students in the PI’s research in collaboration with The Oklahoma Louis Stokes Alliance for Minority Participation; and (iv) develop an undergraduate and an advanced doctoral course.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.

人工智能和无线传感器技术的最新进展导致了合作优化的重大研究。在此制度中，多个代理（例如处理器或传感器）与邻居在本地传达其信息，以协调优化全球性能指标。该分散的范式在与集中协调员的通信是不受欢迎或不可能的网络域中起着关键作用。正是由于这些原因，分散优化方法的设计和性能分析吸引了越来越多的应用领域，例如数据科学，无线网络和通信网络。该项目旨在开发新的模型，数学工具和计算算法，以解决新兴的复杂多代理系统。这种复杂性出现在新兴应用中，例如遥感，具有可再生能源的经济调度模型以及运输网络的效率估算。该提案有可能大大减少复杂多代理网络的理论与现实世界实践之间的差距。此外，与工业合作伙伴的合作将促进有效的知识转移。该项目还旨在通过几项完全集成的教育和外展活动来提高高中生，教育工作者和大学生的意识和兴趣。其中包括加强斯蒂尔沃特高中教师的专业发展，使中学学生从事课后活动，并通过参与不足的本科生研究来促进多样性。长期的研究目标是推进新兴复杂多代理网络中分布式约束优化的计算模型和算法。为了实现这一目标，这项职业建议的研究目标是应用变分不平等的理论，并在分布式优化领域受到监管，以设计具有可证明性能保证的新算法，该算法可以保证可以解决具有复杂约束的多机构网络。这种复杂性出现在多个应用程序域，例如无线传感器网络，传输网络和机器学习，其中优化模型由于存在：（1）约束中的不确定性和非线性； （2）内部大规模优化问题；或（3）等效约束。最新的方法包括加权平衡共识，推送和替代方向乘数方法通常在功能约束易于项目的前提下工作。这些方案很大程度上依赖于拉格朗日二元理论，并且不适合异步方案和交流延迟。根据这项研究，预计将通过以下方式推进复杂网络上的分布式优化领域：（i）通过利用变异不平等理论来开发增强的数学建模框架； （ii）设计和分析具有明确性能界限的新类别基于共识的算法，以解决所提出的建模框架； （iii）探索在拟议的建模框架中解决非平滑度的新颖方法。长期的教育目标是扩大在运营研究和应用数学领域的K-12和大学生（尤其是女性和代表性少数族裔）的参与。为了实现这一目标，这项职业建议的教育目标是激发和吸引年轻人的思想，正式和非正式的教育者以及本科生和研究生，以了解优化在明天实践中的作用。这包括以下活动：（i）为中学教师提供为期四周的专业发展研讨会； （ii）为斯蒂尔沃特高中学生开发一项课后STEM计划； （iii）与俄克拉荷马州路易斯·斯托克斯联盟（Oklahoma Louis Stokes Alliance）合作，参与PI研究的代表性不足的本科生； （iv）发展本科生和高级博士课程。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。