Ergodicity, Output-Controllability, and Antithetic Integral Control of Uncertain Stochastic Reaction Networks

抗扰动的平稳性和跟踪性在抗性积分控制中的随机生化反应网络

Robust ergodicity and tracking in antithetic integral control of stochastic biochemical reaction networks

本文研究了抗性积分控制（AIC）在随机生化反应网络中的鲁棒平稳性和跟踪问题，通过两种方法验证了大规模网络的平稳性和可控性条件。

随机生物分子网络中合成反向积分控制器的鲁棒性和结构性遍历性分析

Robust and structural ergodicity analysis of stochastic biomolecular networks involving synthetic antithetic integral controllers

本文研究了包含合成反向积分控制器的随机生物分子网络的鲁棒性和结构性遍历性分析，提出了一种基于代数和多项式技术的精确理论方法来验证遍历性和输出可控性条件。

随机性反应网络中延迟的遍历性分析与抗性积分控制

Ergodicity analysis and antithetic integral control of a class of stochastic reaction networks with delays

本文研究了一类具有延迟的随机反应网络的遍历性分析和抗性积分控制，证明了相位型分布的延迟不会影响反应网络的遍历性，并展示了延迟对动量方程的影响。

Controllability and ergodicity of 3D primitive equations driven by a finite-dimensional force

We study the problems of controllability and ergodicity of the system of 3D primitive equations modeling large-scale oceanic and atmospheric motions. The system is driven by an additive force acting only on a finite number of Fourier modes in the temperature equation. We first show that the velocity and temperature components of the equations can be simultaneously approximately controlled to arbitrary position in the phase space. The proof is based on Agrachev-Sarychev type geometric control approach. Next, we study the controllability of the linearisation of primitive equations around a non-s…

Ergodicity for the randomly forced Navier-Stokes system in a two-dimensional unbounded domain

The ergodic properties of the randomly forced Navier-Stokes system have been extensively studied in the literature during the last two decades. The problem has always been considered in bounded domains, in order to have, for example, suitable spectral properties for the Stokes operator, to ensure some compactness properties for the resolving operator of the system and the associated functional spaces, etc. In the present paper, we consider the Navier-Stokes system in an unbounded domain satisfying the Poincaré inequality. Assuming that the system is perturbed by a bounded non-degenerate noise,…

隐马尔可夫模型中滤波稳定性的对偶理论

Duality Theory for Filter Stability in Hidden Markov Models

本文针对有限状态离散时间隐马尔可夫模型，建立以倒向随机差分方程为对偶控制系统的对偶理论，推导不变性原理并将其应用于滤波稳定性与收敛速率分析。