Rate-cost tradeoffs in continuous-time control with a biomolecular application

2025-10-24

AI Summary

This paper investigates fundamental limits of rate-constrained continuous-time control in molecular biological systems, specifically for concentration fluctuation suppression under a generalized Ornstein–Uhlenbeck model. Method: It jointly models additive and multiplicative control inputs alongside state-dependent noise, establishing an intrinsic trade-off between control cost and communication data rate. Contribution/Results: The work derives, for the first time, a tight lower bound on the minimum data rate required to achieve a prescribed quadratic control performance; furthermore, it proves that this bound is achievable over an additive white Gaussian noise channel. The results characterize fundamental performance limits of molecular regulation in synthetic biology and provide an information-theoretic foundation and optimality benchmark for feedback control design based on chemical reaction networks.

Technology Category

• Machine Learning: Information Theory
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements

Abstract

This paper focuses on rate-limited control of the generalized Ornstein-Uhlenbeck process where the control action can be either multiplicative or additive, and the noise variance can depend on the control action. We derive a lower bound on the data rate necessary to achieve the desired control cost. The lower bound is attained with equality if the control is performed via an additive white Gaussian channel. The system model approximates the dynamics of a discrete-state molecular birth-death process, and the result has direct implications on the control of a biomolecular system via chemical reactions, where the multiplicative control corresponds to the degradation rate, the additive control corresponds to the production rate, and the control objective is to decrease the fluctuations of the controlled molecular species around their desired concentration levels.

Problem

• Determining minimum data rate for controlling Ornstein-Uhlenbeck process cost
• Analyzing rate-cost tradeoffs in multiplicative and additive control systems
• Applying control theory to reduce biomolecular concentration fluctuations

Innovation

• Lower bound on data rate for control cost
• Additive Gaussian channel achieves optimal bound
• Control molecular fluctuations via chemical reactions