Biomolecular LQR under Partial Observation

Xiaoyu Zhang; Zhou Fang

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arXiv · 2511.02418

Biomolecular LQR under Partial Observation

Xiaoyu Zhang·Zhou Fang

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Abstract

This paper introduces a biomolecular Linear Quadratic Regulator (LQR) to investigate the design principles of gene regulatory networks. We show that for fundamental gene regulation network, the bio-controller derived from LQR theory precisely recapitulate natural network motifs, such as auto-regulation and incoherent feedforward loops. This emulation arises from a fundamental principle: the LQR cost function mathematically encodes environmental survival demands, which subsequently drives the selection of both network topology and biochemical parameters. Our work thus establishes a theoretical basis for interpreting biological circuit design, directly linking evolutionary pressures to observable regulatory structures.

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Xiaoyu Zhang, Zhou Fang. 2025-11-04. Biomolecular LQR under Partial Observation. https://arxiv.org/abs/2511.02418

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