# Minimax Linear Optimal Control of Positive Systems

arXiv: https://arxiv.org/abs/2312.04990 · HTML: https://mlsanity.com/paper/2312.04990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2023.

## Built on by (most cited first, 1 of 1)

- [Sub-optimality of the Separation Principle for Quadratic Control from Bilinear Observations](https://mlsanity.com/paper/2504.11555/) (2025)

## Abstract (arXiv)

We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the Bellman equation can be obtained, revealing that the optimal control policy (among all possible policies) is linear. This policy can in turn be computed through standard value iterations. Moreover, the feedback matrix of the optimal controller inherits the sparsity structure from the constraint matrix of the problem statement. This permits structural controller constraints in the problem design and simplifies the application to large-scale systems. We use a simple example of voltage control in an electric network to illustrate the problem setup.