Model-Free Nonlinear Feedback Optimization

• 成果类型: Article
• 署名作者: He, Zhiyu; Bolognani, Saverio; He, Jianping; Dorfler, Florian; Guan, Xinping
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Shanghai Jiao Tong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3341752
• 发表日期: 2024
• 页码: 4554-4569
• 关键词: Optimization; steady-state; sensitivity; Real-time systems; Power system dynamics; nonlinear dynamical systems; estimation; Autonomous optimization; gradient estimation; Nonconvex Optimization

摘要

Feedback optimization is a control paradigm that enables physical systems to autonomously reach efficient operating points. Its central idea is to interconnect optimization iterations in a closed loop with the physical plant. Since iterative gradient-based methods are extensively used to achieve optimality, feedback optimization controllers typically require knowledge of the steady-state sensitivity of the plant, which may not be easily accessible in some applications. In contrast, in this article, we develop a model-free feedback controller for efficient steady-state operation of general dynamical systems. The proposed design consists of updating control inputs via gradient estimates constructed from evaluations of the nonconvex objective at the current input and at the measured output. We study the dynamic interconnection of the proposed iterative controller with a stable nonlinear discrete-time plant. For this setup, we characterize the optimality and stability of the closed-loop behavior as functions of the problem dimension, the number of iterations, and the rate of convergence of the physical plant. To handle general constraints that affect multiple inputs, we enhance the controller with Frank-Wolfe-type updates.