CAREER: Interplay between Convex and Nonconvex Optimization for Control

职业：凸和非凸优化控制之间的相互作用

• 批准号: 2340713
• 负责人: Yang Zheng
• 金额: $ 55万
• 依托单位: University of California-San Diego
• 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: 2024-05-01 至 2029-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2340713&HistoricalAwards=false
• 关键词: CAREER; Interplay; between; Convex; Nonconvex

Feedback is a fundamental principle underlying many self-regulating natural and technological systems. Control as the principled use of feedback loops and algorithms has been deeply embedded in many engineering systems, including aerospace, energy, transportation, healthcare, and robotic systems. This CAREER project will tackle fundamental challenges related to the interplay between convex and nonconvex optimization for modern control systems. On the one hand, convex reformulations or relaxations have gained popularity in control, thanks to advances in interior-point algorithms. While these methods often provide rigorous stability and safety certificates, their applicability tends to be limited to individual dynamic systems or centralized settings. On the other hand, the old topic of policy search for directly optimiz to empirical successes of reinforcement learning. This class of methods is conceptually simpler, computationally more flexible, but leads to nonconvex optimization, making it harder to derive theoretical guarantees. This project will establish theoretical and algorithmic foundations for bridging convex and nonconvex optimization for a broader class of modern control systems. The outcomes will significantly broaden the optimization and control problems in societal engineering systems, including transportation, power grids, and smart buildings, facilitating efficient and reliable solutions. The project tightly integrates comprehensive educational and outreach activities. A suite of curriculum materials for control education will be developed, lowering the barrier to understanding fundamental feedback principles. The project team will lead activities in summer training camps and collaborate with well-established programs at UCSD, contributing to knowledge dissemination to the general public and K-12 students.This project consists of three synergistic thrusts, fully investigating the interplay between convex and nonconvex optimization for modern control. First, we will develop an innovative framework to reveal hidden convexity in nonconvex static and dynamic distributed control of networked systems. Our framework will advance closed-loop convexity, sparsity invariance, and efficient formulations of linear matrix inequalities. Second, we will establish theoretical guarantees and algorithmic foundations for nonconvex policy search. Specifically, we will develop convex lifting analysis to certify global optimality in smooth nonconvex optimal control and establish algorithmic foundations for nonsmooth and nonconvex robust control with robustness and safety requirements. Lastly, we will develop scalable convex and nonconvex optimization algorithms for large-scale systems by leveraging nonsmooth eigenvalue optimization, decomposition, and acceleration schemes. Collectively, these advances will result in new foundational theoretical frameworks and practical scalable algorithms to achieve reliable and efficient modern control of societal engineering systems.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.

反馈是许多自我调节的自然和技术系统的基本原则。控制反馈回路和算法的原则使用已被深深地嵌入许多工程系统中，包括航空航天，能源，运输，医疗保健和机器人系统。该职业项目将应对与现代控制系统相互作用相互作用相关的基本挑战。一方面，由于室内点算法的进步，凸的重复或放松在控制方面已受欢迎。尽管这些方法通常提供严格的稳定性和安全证书，但它们的适用性往往仅限于单个动态系统或集中设置。另一方面，政策的旧话题直接优化了增强学习的经验成功。这类方法在概念上更简单，在计算上更灵活，但是导致非convex优化，因此很难得出理论保证。该项目将为桥接凸的理论和算法基础建立，用于桥接凸和非凸的优化，以优化一类更广泛的现代控制系统。结果将大大扩大社会工程系统的优化和控制问题，包括运输，电网和智能建筑，促进有效且可靠的解决方案。该项目紧密整合了全面的教育和外展活动。将开发一套用于控制教育的课程材料，从而降低理解基本反馈原则的障碍。该项目团队将在夏季训练营中领导活动，并与UCSD的良好计划合作，为公众和K-12学生的知识传播。该项目由三个协同的推力组成，充分研究了CONVEX与非Conconvex之间的相互作用现代控制的优化。首先，我们将开发一个创新的框架，以揭示NonConvex静态和动态分布式控制系统中隐藏的凸度。我们的框架将提高闭环凸，稀疏性不变性以及线性基质不等式的有效公式。其次，我们将为非convex策略搜索建立理论保证和算法基础。具体而言，我们将开发凸起分析，以证明平滑的非convex最佳控制中的全球最优性，并建立算法基础，以符合鲁棒性和安全要求，为非平滑和非凸的稳健控制。最后，我们将通过利用非滑动特征值优化，分解和加速度方案来开发用于大规模系统的可扩展凸和非凸优化算法。总的来说，这些进步将导致新的基础理论框架和实用的可扩展算法，以实现对社会工程系统的可靠，有效的现代化控制。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和更广泛的影响来支持的，审查标准。