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

Ioannis Tzortzis, Charalambos D. Charalambous, Themistoklis Charalambous, Christoforos N. Hadjicostis, Mikael Johansson

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

Abstrakti

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 optimisation 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.
AlkuperäiskieliEnglanti
Sivut1030-1045
Sivumäärä16
JulkaisuIEEE Transactions on Automatic Control
Vuosikerta62
Numero3
DOI - pysyväislinkit
TilaJulkaistu - 2017
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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