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**Harvard**

Tzortzis, I., Charalambous, C., Charalambous, T., Hadjicostis, C. och Johansson, M. (2017) *Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics*.

** BibTeX **

@article{

Tzortzis2017,

author={Tzortzis, I. and Charalambous, C. D. and Charalambous, Themistoklis and Hadjicostis, C. N. and Johansson, M.},

title={Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics},

journal={IEEE Transactions on Automatic Control},

issn={0018-9286},

volume={62},

issue={3},

pages={1030-1045},

abstract={The aim of this paper is to approximate a Finite-State Markov (FSM) process by another process defined on a lower dimensional state space, called the approximating process, with respect to a total variation distance fidelity criterion. The approximation problem is formulated as an optimization problem using two different approaches. The first approach is based on approximating the transition probability matrix of the FSM process by a lower-dimensional transition probability matrix, resulting in an approximating process which is a Finite-State Hidden Markov (FSHM) process. The second approach is based on approximating the invariant probability vector of the original FSM process by another invariant probability vector defined on a lower-dimensional state space. Going a step further, a method is proposed based on optimizing a Kullback-Leibler divergence to approximate the FSHM processes by FSM processes. The solutions of these optimization problems are described by optimal partition functions which aggregate the states of the FSM process via a corresponding water-filling solution, resulting in lower-dimensional approximating processes which are FSHM or FSM processes. Throughout the paper, the theoretical results are justified by illustrative examples that demonstrate our proposed methodology.},

year={2017},

keywords={Approximating process, Markov process, total variation distance, water-filling, model-reduction, aggregation, Automation & Control Systems, Engineering },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 248736

A1 Tzortzis, I.

A1 Charalambous, C. D.

A1 Charalambous, Themistoklis

A1 Hadjicostis, C. N.

A1 Johansson, M.

T1 Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics

YR 2017

JF IEEE Transactions on Automatic Control

SN 0018-9286

VO 62

IS 3

SP 1030

OP 1045

AB The aim of this paper is to approximate a Finite-State Markov (FSM) process by another process defined on a lower dimensional state space, called the approximating process, with respect to a total variation distance fidelity criterion. The approximation problem is formulated as an optimization problem using two different approaches. The first approach is based on approximating the transition probability matrix of the FSM process by a lower-dimensional transition probability matrix, resulting in an approximating process which is a Finite-State Hidden Markov (FSHM) process. The second approach is based on approximating the invariant probability vector of the original FSM process by another invariant probability vector defined on a lower-dimensional state space. Going a step further, a method is proposed based on optimizing a Kullback-Leibler divergence to approximate the FSHM processes by FSM processes. The solutions of these optimization problems are described by optimal partition functions which aggregate the states of the FSM process via a corresponding water-filling solution, resulting in lower-dimensional approximating processes which are FSHM or FSM processes. Throughout the paper, the theoretical results are justified by illustrative examples that demonstrate our proposed methodology.

LA eng

DO 10.1109/tac.2016.2578299

LK http://dx.doi.org/10.1109/tac.2016.2578299

OL 30