Mixed $H_2/H_{\infty}$ Control Control of Delayed Markov Jump Linear Systems

鲁棒分布式稳定化马尔可夫跳跃大系统：一种邻近模式依赖控制方法

Robust Decentralized Stabilization of Markovian Jump Large-Scale Systems: A Neighboring Mode Dependent Control Approach

本文研究不确定大系统在马尔可夫跳跃参数下的分布式稳定化问题，提出基于局部子系统状态和邻近模式信息的控制方法，并通过数值例子验证理论。

局部模式依赖的去中心化H∞控制不确定马尔可夫跳跃大系统

Local Mode Dependent Decentralized $H_{\infty}$ Control of Uncertain Markovian Jump Large-scale Systems

本文研究了不确定马尔可夫跳跃大系统的去中心化状态反馈控制器H∞鲁棒控制问题，提出基于局部系统状态和局部系统运行模式的充分条件，通过秩约束线性矩阵不等式设计控制器，并通过数值例子验证理论。

Certainty Equivalent Quadratic Control for Markov Jump Systems

Real-world control applications often involve complex dynamics subject to abrupt changes or variations. Markov jump linear systems (MJS) provide a rich framework for modeling such dynamics. Despite an extensive history, theoretical understanding of parameter sensitivities of MJS control is somewhat lacking. Motivated by this, we investigate robustness aspects of certainty equivalent model-based optimal control for MJS with quadratic cost function. Given the uncertainty in the system matrices and in the Markov transition matrix is bounded by $ε$ and $η$ respectively, robustness results are esta…

A Variational Expectation-Maximisation Algorithm for Learning Jump Markov Linear Systems

Jump Markov linear systems (JMLS) are a useful class which can be used to model processes which exhibit random changes in behavior during operation. This paper presents a numerically stable method for learning the parameters of jump Markov linear systems using the expectation-maximisation (EM) approach. The solution provided herein is a deterministic algorithm, and is not a Monte Carlo based technique. As a result, simulations show that when compared to alternative approaches, a more likely set of system parameters can be found within a fixed computation time, which better explain the observat…

算子学习用于线性马尔可夫跳跃超双曲偏微分方程的鲁棒稳定化

Operator Learning for Robust Stabilization of Linear Markov-Jumping Hyperbolic PDEs

本文提出利用算子学习和背stepping方法，通过神经算子近似改进计算效率，实现具有马尔可夫跳跃参数不确定性的双曲PDE的鲁棒稳定化。

Bayesian Parameter Identification for Jump Markov Linear Systems

This paper presents a Bayesian method for identification of jump Markov linear system parameters. A primary motivation is to provide accurate quantification of parameter uncertainty without relying on asymptotic in data-length arguments. To achieve this, the paper details a particle-Gibbs sampling approach that provides samples from the desired posterior distribution. These samples are produced by utilising a modified discrete particle filter and carefully chosen conjugate priors.

Mode Clustering for Markov Jump Systems

In this work, we consider the problem of mode clustering in Markov jump models. This model class consists of multiple dynamical modes with a switching sequence that determines how the system switches between them over time. Under different active modes, the observations can have different characteristics. Given the observations only and without knowing the mode sequence, the goal is to cluster the modes based on their transition distributions in the Markov chain to find a reduced-rank Markov matrix that is embedded in the original Markov chain. Our approach involves mode sequence estimation, m…

带延迟更新的随机逼近：马尔可夫采样下的有限时间速率

Stochastic Approximation with Delayed Updates: Finite-Time Rates under Markovian Sampling

针对多智能体强化学习，研究了马尔可夫采样下带延迟更新的随机逼近算法的有限时间性能，证明了最后迭代指数收敛并达到紧界，且提出无需延迟先验知识的自适应方案以减轻最大延迟影响。

Analysis of Markov Jump Processes under Terminal Constraints

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way the algorithm learns a well-justified finite-state projectio…