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Minimax Linear Regulator Problems for Positive Systems
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DOI：10.1109/tac.2026.3673160.png)
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Abstract
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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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula>-induced gain of the system is studied. We motivate the prospective scalability properties of our framework with a large-scale water management network.
Keywords:
Dynamic programming
large-scale systems
minimax
optimal control
robust control
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W
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Cited Papers