# Mode Reduction for Markov Jump Systems

arXiv: https://arxiv.org/abs/2205.02697 · HTML: https://mlsanity.com/paper/2205.02697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 57 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 13 of 13)

- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Optimal steering of a linear stochastic system to a final probability distribution](https://mlsanity.com/paper/1408.2222/) (2014)
- [Spectral State Compression of Markov Processes](https://mlsanity.com/paper/1802.02920/) (2018)
- [Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds](https://mlsanity.com/paper/2111.07018/) (2021)
- [Optimal Covariance Control for Stochastic Systems Under Chance Constraints](https://mlsanity.com/paper/1804.02829/) (2018)
- [Finite-Horizon Covariance Control of Linear Time-Varying Systems](https://mlsanity.com/paper/1707.04729/) (2017)
- [Approximate Abstractions of Markov Chains with Interval Decision Processes (Extended Version)](https://mlsanity.com/paper/1804.08554/) (2018)
- [Mode Clustering for Markov Jump Systems](https://mlsanity.com/paper/1910.02193/) (2019)
- [On the Relationship between Bisimulation and Trace Equivalence in an Approximate Probabilistic Context (Extended Version)](https://mlsanity.com/paper/1701.04547/) (2017)
- [Certainty Equivalent Quadratic Control for Markov Jump Systems](https://mlsanity.com/paper/2105.12358/) (2021)
- [Ensemble Control of Time-Invariant Linear Systems with Linear Parameter Variation](https://mlsanity.com/paper/1410.1456/) (2014)
- [Approximations of Stochastic Hybrid Systems: A Compositional Approach](https://mlsanity.com/paper/1508.06496/) (2015)

## Abstract (arXiv)

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.