Log-Barrier Search for Structural Linear Quadratic Regulators

• Published in: IEEE transactions on automatic control Vol. 70; no. 3; pp. 1965 - 1972
• Main Authors: Yang, Nachuan, Tang, Jiawei, Li, Yuzhe, Shi, Guodong, Shi, Ling
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Algorithms; Convergence; Covariance matrices; Kuhn-Tucker method; Linear quadratic regulator; Linear quadratic regulator (LQR); Optimal control; Optimization; Output feedback; Regulators; Sensor systems; Service robots; Sparse matrices; State feedback; structural gain; Topology; Transforms; Transportation
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3482097

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.