Minimax Linear Regulator Problems for Positive Systems

• 成果类型: Article
• 署名作者: Gurpegui, Alba; Jeeninga, Mark; Tegling, Emma; Rantzer, Anders
• 署名单位: Lund University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3673160
• 发表日期: 2026
• 关键词: LYAPUNOV FUNCTIONS

摘要

Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work considers a multidisturbance minimax linear regulator (LR) framework for positive linear time-invariant systems in continuous time, which, analogous to the linear-quadratic regulator problem, can be utilized for the stabilization of positive systems. The problem is studied for nonnegative and state-bounded disturbances. Dynamic programming theory is leveraged to derive explicit solutions to the minimax LR problem for both finite and infinite time horizons. In addition, a fixed-point method is proposed that computes the solution for the infinite horizon case, and the minimum $L_{1}$-induced gain of the system is studied. We motivate the prospective scalability properties of our framework with a large-scale water management network.