Mode Reduction for Markov Jump Systems

TL;DR

This paper introduces a clustering-based method to reduce the number of modes in Markov jump linear systems, enabling simpler models that maintain accuracy for stability analysis and controller design, thus lowering computational costs.

Contribution

It proposes a novel mode reduction technique for MJSs using clustering, addressing a less-studied aspect of system complexity reduction.

Findings

Reduced MJSs approximate original systems well under various metrics.

The approach significantly lowers computational costs in stability analysis.

The method guarantees accuracy in controller design using the reduced models.

Abstract

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.