Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting

• 成果类型: Article
• 署名作者: Zheng, Yang; Pai, Chih-Fan Rich; Tang, Yujie
• 署名单位: University of California System; University of California San Diego; Peking University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3675545
• 发表日期: 2026
• 关键词: OUTPUT-FEEDBACK CONTROL; policy optimization; INFINITY; h-2

摘要

Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In Part II of this article, we introduce a new and unified extended convex lifting (ECL) framework to reveal hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL offers a bridge between nonconvex policy optimization and convex reformulations, enabling convex analysis for nonconvex problems. Despite nonconvexity and nonsmoothness, the existence of an ECL not only reveals that minimizing the original function is equivalent to a convex problem but also certifies a class of first-order nondegenerate stationary points to be globally optimal. This ECL framework can cover many benchmark control problems, including linear quadratic regulator, linear quadratic Gaussian, and H-infinity robust control. We also believe that the new ECL framework will be of independent interest for analyzing nonconvex problems beyond control.