Internal Model-Based Online Optimization

• 成果类型: Article
• 署名作者: Bastianello, Nicola; Carli, Ruggero; Zampieri, Sandro
• 署名单位: Royal Institute of Technology; University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3297504
• 发表日期: 2024
• 页码: 689-696
• 关键词: Signal processing algorithms; optimization; Heuristic algorithms; COSTS; trajectory; CONVERGENCE; Approximation algorithms; Digital control; online gradient descent; online optimization; Robust control; structured algorithms

摘要

In this article, we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (nonquadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and nonquadratic problems.