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

TL;DR

This paper establishes fundamental limits on the data rate needed for controlling a stochastic process, with applications to biomolecular systems, by deriving bounds that relate control costs to information rates.

Contribution

It introduces a lower bound on data rate for rate-limited control of a generalized Ornstein-Uhlenbeck process, applicable to biomolecular control systems.

Findings

Lower bound on data rate derived for control performance

Equality achieved with additive Gaussian channel control

Implications for controlling molecular fluctuations

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.