Minimax Linear Regulator Problems for Positive Systems
Abstract
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 multi-disturbance minimax Linear Regulator (LR) framework for positive linear time-invariant systems in continuous time, which, analogous to the Linear-Quadratic Regulator (LQR) 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 L1-induced gain of the system is studied. We motivate the prospective scalability properties of our framework with a large-scale water management network.
Cite
@article{arxiv.2411.04809,
title = {Minimax Linear Regulator Problems for Positive Systems},
author = {Alba Gurpegui and Mark Jeeninga and Emma Tegling and Anders Rantzer},
journal= {arXiv preprint arXiv:2411.04809},
year = {2026}
}
Comments
30 pages, 6 figures. Accepted for publication in IEEE Transactions on Automatic Control