Log-Barrier Search for Structural Linear Quadratic Regulators

• 成果类型: Article
• 署名作者: Yang, Nachuan; Tang, Jiawei; Li, Yuzhe; Shi, Guodong; Shi, Ling
• 署名单位: Hong Kong University of Science & Technology; Northeastern University - China; University of Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3482097
• 发表日期: 2025
• 页码: 1965-1972
• 关键词: convergence; regulators; TOPOLOGY; Sparse matrices; Covariance matrices; actuators; transportation; Transforms; Service robots; Sensor systems; linear quadratic regulator (LQR); optimal control; structural gain

摘要

This article studies the design of linear quadratic regulators (LQR) subject to structural constraints, which remains an NP-hard open problem. Both state-feedback and static output-feedback cases are investigated. Instead of using case-by-case relaxation techniques, we propose a tractable first-order method to solve this structural optimal control problem. More specifically, we equivalently reformulate it as a constrained optimization and characterize its first-order optimality condition via Karush-Kuhn-Tucker conditions. To solve this NP-hard problem, we propose a novel optimization method, called log-barrier search (LBS), which incorporates a modified log-barrier term into the control objective function and adaptively changes its parameters during the computation process. The convergence of our method is theoretically guaranteed and at least a stationary solution can be obtained. We compare the proposed method with other existing algorithms, where the LBS method shows a very competitive performance in both speed and optimality.