Approximation of Markov processes by lower dimensional processes
Ημερομηνία
2014Συγγραφέας
Tzortzis, I.![ORCID logo](https://orcid.org/sites/default/files/images/orcid_16x16.png)
Charalambous, T.
![ORCID logo](https://orcid.org/sites/default/files/images/orcid_16x16.png)
Johansson, M.
Εκδότης
Institute of Electrical and Electronics Engineers Inc.Source
Proceedings of the IEEE Conference on Decision and ControlProceedings of the IEEE Conference on Decision and Control
Volume
2015-FebruaryPages
4441-4446Google Scholar check
Metadata
Εμφάνιση πλήρους εγγραφήςΕπιτομή
In this paper, we investigate the problem of aggregating a given finite-state Markov process by another process with fewer states. The aggregation utilizes total variation distance as a measure of discriminating the Markov process by the aggregate process, and aims to maximize the entropy of the aggregate process invariant probability, subject to a fidelity described by the total variation distance ball. An iterative algorithm is presented to compute the invariant distribution of the aggregate process, as a function of the invariant distribution of the Markov process. It turns out that the approximation method via aggregation leads to an optimal aggregate process which is a hidden Markov process, and the optimal solution exhibits a water-filling behavior. Finally, the algorithm is applied to specific examples to illustrate the methodology and properties of the approximations. © 2014 IEEE.