Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems

Ramen Ghosh; Mahmoud Tahmasebi; Marion McAfee

doi:10.1109/CoDIT58514.2023.10284085

Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems

Ramen Ghosh, Mahmoud Tahmasebi, Marion McAfee

Department of Mechatronic Engineering

Atlantic Technological University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The article aims to demonstrate the effectiveness of using the Koopman operator and dynamic mode decomposition (DMD) for iterated function systems (IFS). Specifically, we show how these tools can be used to analyze and predict the behaviour of stochastic nonlinear dynamical systems represented by discrete-time Markov chains on a compact state space. In particular, we focus on an ergodic nonlinear IFS, which has not been studied with these approaches before. Our paper presents the first application of dynamic mode decomposition to this type of system.

Original language	English
Title of host publication	9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	305-308
Number of pages	4
ISBN (Electronic)	9798350311402
DOIs	https://doi.org/10.1109/CoDIT58514.2023.10284085
Publication status	Published - 2023
Event	9th International Conference on Control, Decision and Information Technologies, CoDIT 2023 - Rome, Italy Duration: 3 Jul 2023 → 6 Jul 2023

Publication series

Name	9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023

Conference

Conference	9th International Conference on Control, Decision and Information Technologies, CoDIT 2023
Country/Territory	Italy
City	Rome
Period	3/07/23 → 6/07/23

Keywords

Data Driven Dynamical System
Dynamic Mode Decomposition
Iterated Function System
Koopman Operator
Non-linear Stochastic Dynamics

Access to Document

10.1109/CoDIT58514.2023.10284085

Cite this

Ghosh, R., Tahmasebi, M., & McAfee, M. (2023). Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems. In 9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023 (pp. 305-308). (9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CoDIT58514.2023.10284085

Ghosh, Ramen ; Tahmasebi, Mahmoud ; McAfee, Marion. / Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems. 9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023. Institute of Electrical and Electronics Engineers Inc., 2023. pp. 305-308 (9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023).

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abstract = "The article aims to demonstrate the effectiveness of using the Koopman operator and dynamic mode decomposition (DMD) for iterated function systems (IFS). Specifically, we show how these tools can be used to analyze and predict the behaviour of stochastic nonlinear dynamical systems represented by discrete-time Markov chains on a compact state space. In particular, we focus on an ergodic nonlinear IFS, which has not been studied with these approaches before. Our paper presents the first application of dynamic mode decomposition to this type of system.",

keywords = "Data Driven Dynamical System, Dynamic Mode Decomposition, Iterated Function System, Koopman Operator, Non-linear Stochastic Dynamics",

author = "Ramen Ghosh and Mahmoud Tahmasebi and Marion McAfee",

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year = "2023",

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Ghosh, R, Tahmasebi, M & McAfee, M 2023, Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems. in 9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023. 9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023, Institute of Electrical and Electronics Engineers Inc., pp. 305-308, 9th International Conference on Control, Decision and Information Technologies, CoDIT 2023, Rome, Italy, 3/07/23. https://doi.org/10.1109/CoDIT58514.2023.10284085

Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems. / Ghosh, Ramen; Tahmasebi, Mahmoud; McAfee, Marion.
9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 305-308 (9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The article aims to demonstrate the effectiveness of using the Koopman operator and dynamic mode decomposition (DMD) for iterated function systems (IFS). Specifically, we show how these tools can be used to analyze and predict the behaviour of stochastic nonlinear dynamical systems represented by discrete-time Markov chains on a compact state space. In particular, we focus on an ergodic nonlinear IFS, which has not been studied with these approaches before. Our paper presents the first application of dynamic mode decomposition to this type of system.

AB - The article aims to demonstrate the effectiveness of using the Koopman operator and dynamic mode decomposition (DMD) for iterated function systems (IFS). Specifically, we show how these tools can be used to analyze and predict the behaviour of stochastic nonlinear dynamical systems represented by discrete-time Markov chains on a compact state space. In particular, we focus on an ergodic nonlinear IFS, which has not been studied with these approaches before. Our paper presents the first application of dynamic mode decomposition to this type of system.

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KW - Dynamic Mode Decomposition

KW - Iterated Function System

KW - Koopman Operator

KW - Non-linear Stochastic Dynamics

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M3 - Conference contribution

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BT - 9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023

PB - Institute of Electrical and Electronics Engineers Inc.

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Ghosh R, Tahmasebi M, McAfee M. Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems. In 9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 305-308. (9th 2023 International Conference on Control, Decision and Information Technologies, CoDIT 2023). doi: 10.1109/CoDIT58514.2023.10284085

Dynamic Mode Decomposition and Koopman Operator for Iterated Function Systems

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