马尔可夫跳变线性系统最优控制的研究现状与进展

马尔可夫跳变线性系统（MJLS）是一种具有多个模态的随机系统，系统在各个模态之间的跳变转移由一组马尔可夫链来决定。MJLS模型因其在表示过程中可以产生突变而更能精确的描述实际工程应用中的系统。近年来，MJLS的最优控制问题成为了研究的热点，动态规划、极大值原理以及线性矩阵不等式等成为了解决此类问题的主流方法。本文对MJLS最优控制领域的研究现状进行了综述。分别对一般情况下、带有噪声的情况下、带有时滞的情况下以及某些特定情况下的MLJS最优控制问题的国内外研究现状进行论述。最后进行了总结并提出MJLS最优控制领域未来值得关注的研究方向。

Recent Status and Progress in Optimal Control of Markov Jump Linear Systems

A Markov jump linear system (MJLS) is a random system with multiple modes. The jump transition of the system between each mode is determined by a set of Markov chains. The MJLS model can accurately describe the system in actual engineering applications because it can produce mutations in the representation process. In recent years, the optimal control problem of the MJLS has become a research hotspot. Dynamic programming, maximum value principle, and linear matrix inequality have become the mainstream methods to solve such problems. This paper reviews the current research status of the MJLS optimal control field. The research status of MLJS optimal control problems at home and abroad under general conditions, noise conditions, time delay conditions, and some specific conditions are discussed individually. Finally, the research direction of the MJLS optimal control field worthy of attention in the future is summarized and put forward.