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.

翻译：本文研究广义Ornstein-Uhlenbeck过程的速率受限控制问题，其中控制作用既可为乘性亦可为加性，且噪声方差可依赖于控制作用。我们推导了实现期望控制成本所需数据速率的下界。当控制通过加性高斯白噪声信道执行时，该下界可达等号成立。该模型近似描述了离散态分子生灭过程的动力学特性，其结论对通过化学反应控制生物分子系统具有直接意义：其中乘性控制对应降解速率，加性控制对应生成速率，控制目标在于降低受控分子物种围绕其期望浓度水平的波动。