[论文解读] Optimization Algorithms as Robust Feedback Controllers

Adrian Hauswirth, He, Zhiyu+3 more|arXiv (Cornell University)|Mar 21, 2021

Extremum Seeking Control Systems被引用 32

一句话总结

本综述将优化算法框定为动态系统和反馈控制器，聚焦数据驱动情境中的闭环稳定性与约束处理，及其在电网和通信中的应用。

ABSTRACT

Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline. Optimization problems are formulated to be solved numerically with specific algorithms running on microprocessors. An emerging alternative is to view optimization algorithms as dynamical systems. Besides being insightful in itself, this perspective liberates optimization methods from specific numerical and algorithmic aspects and opens up new possibilities to endow complex real-world systems with sophisticated self-optimizing behavior. Towards this goal, it is necessary to understand how numerical optimization algorithms can be converted into feedback controllers to enable robust "closed-loop optimization". In this article, we focus on recent control designs under the name of "feedback-based optimization" which implement optimization algorithms directly in closed loop with physical systems. In addition to a brief overview of selected continuous-time dynamical systems for optimization, our particular emphasis in this survey lies on closed-loop stability as well as the robust enforcement of physical and operational constraints in closed-loop implementations. To bypass accessing partial model information of physical systems, we further elaborate on fully data-driven and model-free operations. We highlight an emerging application in autonomous reserve dispatch in power systems, where the theory has transitioned to practice by now. We also provide short expository reviews of pioneering applications in communication networks and electricity grids, as well as related research streams, including extremum seeking and pertinent methods from model predictive and process control, to facilitate high-level comparisons with the main topic of this survey.

研究动机与目标

• 激励并正式化将优化算法视为可与物理系统闭环耦合的动态系统的观点。
• 探讨基于反馈的优化如何在模型不准确和参数随时间变化的情况下实现鲁棒性。
• 审查在闭环优化中执行硬约束和软约束的机制。
• 讨论自我优化的自主系统的数据驱动和模型无关（无模型）运行。
• 突出在自主储备调度及相关领域的应用，以将理论付诸实践。

提出的方法

• 回顾将连续时间优化动力学（如梯度流、投影梯度流和原-对偶鞍点流）作为动态系统的研究。
• 讨论与物理系统的闭环互连以及奇异摄动和稳定性分析的作用。
• 提出约束执行机制，包括投影、抗积分饱和、对偶化和近似投影。
• 概述数据驱动和无模型策略，包括在线灵敏度学习和无导数优化。
• 提供关于电网中实时最优潮流及自动再调度的案例研究。
• 与相关方法如极值寻优、包含不完整优化的模型预测控制（MPC）以及修饰适应进行比较（modifier adaptation）。

实验结果

研究问题

• RQ1 如何将优化算法解释为动态系统并与物理植物闭环集成？
• RQ2 在数据不确定性和参数随时间变化的情况下，闭环优化的稳定性与鲁棒性条件是什么？
• RQ3 在不完全依赖模型的情况下，如何在闭环优化中有效执行硬约束和软约束？
• RQ4 哪些数据驱动或无模型的技术能够实现实时的自主、基于测量的优化？
• RQ5 这些理论如何应用于现实世界的应用，如电力系统中的自主储备调度？

主要发现

• 优化动力学可以与系统耦合，将输出驱动到基于优化器的平衡点。
• 稳定性结果与奇异摄动和鞍点动力学相关，帮助设计稳定的闭环控制器。
• 投影梯度和鞍点流为在闭环设置中处理不等式约束与等式约束提供机制。
• 抗积分饱和和对偶化策略在执行限制和饱和存在时实现约束执行。
• 数据驱动和在线灵敏度学习实现无模型运行，同时保持收敛到最优解。
• 在电力系统中的实时应用展示了用于自治再调度和实时潮流的闭环优化。