Approximation of Markov processes by lower dimensional processes
Ημερομηνία
2014Συγγραφέας
Tzortzis, I.Charalambous, Charalambos D.
Charalambous, T.
Hadjicostis, Christoforos N.
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.