论文标题
马尔可夫跳跃系统的模式减少
Mode Reduction for Markov Jump Systems
论文作者
论文摘要
开关系统能够使用基本动力学进行建模，这些动力可能会随着时间的推移而突然改变。为了实现实践中的准确建模，可能需要大量模式，但这可能会大大提高模型的复杂性。降低系统复杂性的现有工作主要考虑了状态空间的降低，但减少模式的数量的研究较少。在这项工作中，我们考虑Markov跳跃线性系统（MJSS），这是一类特殊的开关系统，其中主动模式根据Markov链进行开关，以及与其模式复杂性相关的几个问题。具体而言，受到无监督学习的聚类技术的启发，我们能够以更少的模式构建减少的MJ，从而在各种指标下构建原始MJ的近似值。此外，从理论和经验上讲，我们展示了如何使用降低的MJ分析稳定性和设计控制器，并显着降低了计算成本，同时实现了保证的准确性。
Switched systems are capable of modeling processes with underlying dynamics that may change abruptly over time. To achieve accurate modeling in practice, one may need a large number of modes, but this may in turn increase the model complexity drastically. Existing work on reducing system complexity mainly considers state space reduction, yet reducing the number of modes is less studied. In this work, we consider Markov jump linear systems (MJSs), a special class of switched systems where the active mode switches according to a Markov chain, and several issues associated with its mode complexity. Specifically, inspired by clustering techniques from unsupervised learning, we are able to construct a reduced MJS with fewer modes that approximates well the original MJS under various metrics. Furthermore, both theoretically and empirically, we show how one can use the reduced MJS to analyze stability and design controllers with significant reduction in computational cost while achieving guaranteed accuracy.
