A regularized kernel-based method for learning a module in a dynamic network with correlated noise

Venkatakrishnan C. Rajagopal, Karthik R. Ramaswamy, Paul M.J. Van Den Hof

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

In this paper, we consider the problem of identifying one system (module) embedded in a dynamic network that is disturbed by colored process noise sources, which can possibly be correlated. To achieve this using the direct method for single module identification, we need to formulate a Multi-Input-Multi-Output (MIMO) estimation problem which requires model order selection step for each module in the setup and estimation of large number of parameters. This results in a larger variance in the estimates and an increase in computation complexity. Therefore, we extend the Empirical Bayes Direct Method [1], which handles the above mentioned problems for a Multi-Input-Single-Output (MISO) setup to a MIMO setting by suitably modifying the framework. We keep a parametric model for the desired target module and model the impulse response of all the other modules as independent zero mean Gaussian process governed by a first-order stable spline kernel. The parameters of the target module are obtained by maximizing the marginal likelihood of the output using the Empirical Bayes (EB) approach. To solve this, we use the Expectation Maximization (EM) algorithm which offers computational advantages. Numerical simulation illustrate the advantages of the developed method over existing classical methods.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers
Pages4348-4353
Number of pages6
ISBN (Electronic)978-1-7281-7447-1
DOIs
Publication statusPublished - 14 Dec 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: 14 Dec 202018 Dec 2020

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
CountryKorea, Republic of
CityVirtual, Jeju Island
Period14/12/2018/12/20

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