Mode Reduction for Markov Jump Systems
This work addresses the mode complexity issue in switched systems, which is important for practitioners in control theory and engineering, though it is incremental as it builds on clustering techniques from unsupervised learning.
The paper tackles the problem of high model complexity in Markov jump linear systems (MJSs) due to a large number of modes, by proposing a method to construct a reduced MJS with fewer modes that approximates the original well under various metrics, resulting in significant reduction in computational cost for stability analysis and controller design while maintaining guaranteed accuracy.
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.