Linear Quadratic Control of Positive Systems: A Projection-Based Approach

• 成果类型: Article
• 署名作者: Yang, Nachuan; Tang, Jiawei; Wong, Yik Ben; Li, Yuzhe; Shi, Ling
• 署名单位: Hong Kong University of Science & Technology; Northeastern University - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3172237
• 发表日期: 2023
• 页码: 2376-2382
• 关键词: Linear systems; control systems; COSTS; uncertainty; Optimization methods; Lenses; Time measurement; linear quadratic regulator (LQR); nonfragile control; positive linear systems; projected gradient descent (PGD)

摘要

This technical article investigates the linear quadratic regulator (LQR) design for continuous-time positive linear systems. Based on positive systems theory and Lyapunov theory, the solvability and optimality of the positivity-preserving LQR problem are analyzed through the lens of optimization, and two projection theorems are derived for single-input and multi-input positive systems, respectively, which paves the way for developing a projected gradient descent algorithm. The proposed results fill the literature gap by considering both the optimality and positivity in LQR design, and numerical simulations are provided to verify the effectiveness of the results.