This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

中文翻译：

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不完全MTPM和MOCPM约束隐马尔可夫跳跃线性系统的异步二次控制

本文研究了具有不完全模态转移概率矩阵（MTPM）的约束马尔可夫跳跃线性系统的二次最优控制问题。考虑到原始系统模式不可访问，观测模式用于异步控制器设计，其中模式观测条件概率矩阵 (MOCPM)，其表征原始模式和观测模式之间的发射被假定为部分已知。为这种具有不完全 MTPM 和 MOCPM 的受限隐马尔可夫跳跃线性系统制定了 LMI 优化问题。在此基础上，可以应用自由连接加权矩阵方法设计一个可行的状态反馈控制器。所需的控制器，取决于观察到的模式，是一种异步方法，可以最小化二次成本的上限并满足对系统状态和控制变量的限制。此外，为了简化计算复杂性，探索了将观察到的模式重铸成几个集群的聚类观察。提供了数值例子来说明有效性。