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arXiv · 2411.04809

Minimax Linear Regulator Problems for Positive Systems

Alba Gurpegui·Mark Jeeninga·Emma Tegling·Anders Rantzer
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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.

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Alba Gurpegui, Mark Jeeninga, Emma Tegling, Anders Rantzer. 2024-11-07. Minimax Linear Regulator Problems for Positive Systems. https://arxiv.org/abs/2411.04809

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