---
_id: '29543'
article_number: '109804'
author:
- first_name: Walid
  full_name: Djema, Walid
  last_name: Djema
- first_name: Laetitia
  full_name: Giraldi, Laetitia
  last_name: Giraldi
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Olivier
  full_name: Bernard, Olivier
  last_name: Bernard
citation:
  ama: Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal
    selection of species represented by quota models. <i>Automatica</i>. 2021;132.
    doi:<a href="https://doi.org/10.1016/j.automatica.2021.109804">10.1016/j.automatica.2021.109804</a>
  apa: Djema, W., Giraldi, L., Maslovskaya, S., &#38; Bernard, O. (2021). Turnpike
    features in optimal selection of species represented by quota models. <i>Automatica</i>,
    <i>132</i>, Article 109804. <a href="https://doi.org/10.1016/j.automatica.2021.109804">https://doi.org/10.1016/j.automatica.2021.109804</a>
  bibtex: '@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features
    in optimal selection of species represented by quota models}, volume={132}, DOI={<a
    href="https://doi.org/10.1016/j.automatica.2021.109804">10.1016/j.automatica.2021.109804</a>},
    number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema,
    Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021}
    }'
  chicago: Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard.
    “Turnpike Features in Optimal Selection of Species Represented by Quota Models.”
    <i>Automatica</i> 132 (2021). <a href="https://doi.org/10.1016/j.automatica.2021.109804">https://doi.org/10.1016/j.automatica.2021.109804</a>.
  ieee: 'W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features
    in optimal selection of species represented by quota models,” <i>Automatica</i>,
    vol. 132, Art. no. 109804, 2021, doi: <a href="https://doi.org/10.1016/j.automatica.2021.109804">10.1016/j.automatica.2021.109804</a>.'
  mla: Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented
    by Quota Models.” <i>Automatica</i>, vol. 132, 109804, Elsevier BV, 2021, doi:<a
    href="https://doi.org/10.1016/j.automatica.2021.109804">10.1016/j.automatica.2021.109804</a>.
  short: W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).
date_created: 2022-01-26T13:13:06Z
date_updated: 2022-01-26T13:15:33Z
department:
- _id: '636'
doi: 10.1016/j.automatica.2021.109804
intvolume: '       132'
keyword:
- Electrical and Electronic Engineering
- Control and Systems Engineering
language:
- iso: eng
publication: Automatica
publication_identifier:
  issn:
  - 0005-1098
publication_status: published
publisher: Elsevier BV
status: public
title: Turnpike features in optimal selection of species represented by quota models
type: journal_article
user_id: '87909'
volume: 132
year: '2021'
...
---
_id: '10593'
abstract:
- lang: eng
  text: We present a new framework for optimal and feedback control of PDEs using
    Koopman operator-based reduced order models (K-ROMs). The Koopman operator is
    a linear but infinite-dimensional operator which describes the dynamics of observables.
    A numerical approximation of the Koopman operator therefore yields a linear system
    for the observation of an autonomous dynamical system. In our approach, by introducing
    a finite number of constant controls, the dynamic control system is transformed
    into a set of autonomous systems and the corresponding optimal control problem
    into a switching time optimization problem. This allows us to replace each of
    these systems by a K-ROM which can be solved orders of magnitude faster. By this
    approach, a nonlinear infinite-dimensional control problem is transformed into
    a low-dimensional linear problem. Using a recent convergence result for the numerical
    approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the
    value of the K-ROM based objective function converges in measure to the value
    of the full objective function. To illustrate the results, we consider the 1D
    Burgers equation and the 2D Navier–Stokes equations. The numerical experiments
    show remarkable performance concerning both solution times and accuracy.
article_type: original
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
citation:
  ama: Peitz S, Klus S. Koopman operator-based model reduction for switched-system
    control of PDEs. <i>Automatica</i>. 2019;106:184-191. doi:<a href="https://doi.org/10.1016/j.automatica.2019.05.016">10.1016/j.automatica.2019.05.016</a>
  apa: Peitz, S., &#38; Klus, S. (2019). Koopman operator-based model reduction for
    switched-system control of PDEs. <i>Automatica</i>, <i>106</i>, 184–191. <a href="https://doi.org/10.1016/j.automatica.2019.05.016">https://doi.org/10.1016/j.automatica.2019.05.016</a>
  bibtex: '@article{Peitz_Klus_2019, title={Koopman operator-based model reduction
    for switched-system control of PDEs}, volume={106}, DOI={<a href="https://doi.org/10.1016/j.automatica.2019.05.016">10.1016/j.automatica.2019.05.016</a>},
    journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019},
    pages={184–191} }'
  chicago: 'Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction
    for Switched-System Control of PDEs.” <i>Automatica</i> 106 (2019): 184–91. <a
    href="https://doi.org/10.1016/j.automatica.2019.05.016">https://doi.org/10.1016/j.automatica.2019.05.016</a>.'
  ieee: S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system
    control of PDEs,” <i>Automatica</i>, vol. 106, pp. 184–191, 2019.
  mla: Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction
    for Switched-System Control of PDEs.” <i>Automatica</i>, vol. 106, 2019, pp. 184–91,
    doi:<a href="https://doi.org/10.1016/j.automatica.2019.05.016">10.1016/j.automatica.2019.05.016</a>.
  short: S. Peitz, S. Klus, Automatica 106 (2019) 184–191.
date_created: 2019-07-10T08:08:16Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1016/j.automatica.2019.05.016
intvolume: '       106'
language:
- iso: eng
page: 184-191
publication: Automatica
publication_identifier:
  issn:
  - 0005-1098
publication_status: published
status: public
title: Koopman operator-based model reduction for switched-system control of PDEs
type: journal_article
user_id: '47427'
volume: 106
year: '2019'
...
---
_id: '15741'
abstract:
- lang: eng
  text: "\r\nIn many cyber–physical systems, we encounter the problem of remote state
    estimation of geo- graphically distributed and remote physical processes. This
    paper studies the scheduling of sensor transmissions to estimate the states of
    multiple remote, dynamic processes. Information from the different sensors has
    to be transmitted to a central gateway over a wireless network for monitoring
    purposes, where typically fewer wireless channels are available than there are
    processes to be monitored. For effective estimation at the gateway, the sensors
    need to be scheduled appropriately, i.e., at each time instant one needs to decide
    which sensors have network access and which ones do not. To address this scheduling
    problem, we formulate an associated Markov decision process (MDP). This MDP is
    then solved using a Deep Q-Network, a recent deep reinforcement learning algorithm
    that is at once scalable and model-free. We compare our scheduling algorithm to
    popular scheduling algorithms such as round-robin and reduced-waiting-time, among
    others. Our algorithm is shown to significantly outperform these algorithms for
    many example scenario"
article_number: '108759'
author:
- first_name: Alex S.
  full_name: Leong, Alex S.
  last_name: Leong
- first_name: Arunselvan
  full_name: Ramaswamy, Arunselvan
  id: '66937'
  last_name: Ramaswamy
  orcid: https://orcid.org/ 0000-0001-7547-8111
- first_name: Daniel E.
  full_name: Quevedo, Daniel E.
  last_name: Quevedo
- first_name: Holger
  full_name: Karl, Holger
  id: '126'
  last_name: Karl
- first_name: Ling
  full_name: Shi, Ling
  last_name: Shi
citation:
  ama: Leong AS, Ramaswamy A, Quevedo DE, Karl H, Shi L. Deep reinforcement learning
    for wireless sensor scheduling in cyber–physical systems. <i>Automatica</i>. 2019.
    doi:<a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>
  apa: Leong, A. S., Ramaswamy, A., Quevedo, D. E., Karl, H., &#38; Shi, L. (2019).
    Deep reinforcement learning for wireless sensor scheduling in cyber–physical systems.
    <i>Automatica</i>. <a href="https://doi.org/10.1016/j.automatica.2019.108759">https://doi.org/10.1016/j.automatica.2019.108759</a>
  bibtex: '@article{Leong_Ramaswamy_Quevedo_Karl_Shi_2019, title={Deep reinforcement
    learning for wireless sensor scheduling in cyber–physical systems}, DOI={<a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>},
    number={108759}, journal={Automatica}, author={Leong, Alex S. and Ramaswamy, Arunselvan
    and Quevedo, Daniel E. and Karl, Holger and Shi, Ling}, year={2019} }'
  chicago: Leong, Alex S., Arunselvan Ramaswamy, Daniel E. Quevedo, Holger Karl, and
    Ling Shi. “Deep Reinforcement Learning for Wireless Sensor Scheduling in Cyber–Physical
    Systems.” <i>Automatica</i>, 2019. <a href="https://doi.org/10.1016/j.automatica.2019.108759">https://doi.org/10.1016/j.automatica.2019.108759</a>.
  ieee: A. S. Leong, A. Ramaswamy, D. E. Quevedo, H. Karl, and L. Shi, “Deep reinforcement
    learning for wireless sensor scheduling in cyber–physical systems,” <i>Automatica</i>,
    2019.
  mla: Leong, Alex S., et al. “Deep Reinforcement Learning for Wireless Sensor Scheduling
    in Cyber–Physical Systems.” <i>Automatica</i>, 108759, 2019, doi:<a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>.
  short: A.S. Leong, A. Ramaswamy, D.E. Quevedo, H. Karl, L. Shi, Automatica (2019).
date_created: 2020-01-31T15:55:27Z
date_updated: 2022-01-06T06:52:32Z
ddc:
- '000'
department:
- _id: '7'
- _id: '34'
- _id: '3'
- _id: '75'
- _id: '57'
doi: 10.1016/j.automatica.2019.108759
file:
- access_level: closed
  content_type: application/pdf
  creator: hkarl
  date_created: 2020-01-31T15:57:50Z
  date_updated: 2020-01-31T15:57:50Z
  file_id: '15743'
  file_name: leoram20a.pdf
  file_size: '675382'
  relation: main_file
  success: 1
file_date_updated: 2020-01-31T15:57:50Z
has_accepted_license: '1'
language:
- iso: eng
project:
- _id: '24'
  name: Netzgewahre Regelung & regelungsgewahre Netze
publication: Automatica
publication_identifier:
  issn:
  - 0005-1098
publication_status: published
quality_controlled: '1'
status: public
title: Deep reinforcement learning for wireless sensor scheduling in cyber–physical
  systems
type: journal_article
user_id: '126'
year: '2019'
...
---
_id: '35583'
article_number: '108759'
author:
- first_name: Alex S.
  full_name: Leong, Alex S.
  last_name: Leong
- first_name: Arunselvan
  full_name: Ramaswamy, Arunselvan
  last_name: Ramaswamy
- first_name: Daniel E.
  full_name: Quevedo, Daniel E.
  last_name: Quevedo
- first_name: Holger
  full_name: Karl, Holger
  last_name: Karl
- first_name: Ling
  full_name: Shi, Ling
  last_name: Shi
citation:
  ama: Leong AS, Ramaswamy A, Quevedo DE, Karl H, Shi L. Deep reinforcement learning
    for wireless sensor scheduling in cyber–physical systems. <i>Automatica</i>. 2019;113.
    doi:<a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>
  apa: Leong, A. S., Ramaswamy, A., Quevedo, D. E., Karl, H., &#38; Shi, L. (2019).
    Deep reinforcement learning for wireless sensor scheduling in cyber–physical systems.
    <i>Automatica</i>, <i>113</i>, Article 108759. <a href="https://doi.org/10.1016/j.automatica.2019.108759">https://doi.org/10.1016/j.automatica.2019.108759</a>
  bibtex: '@article{Leong_Ramaswamy_Quevedo_Karl_Shi_2019, title={Deep reinforcement
    learning for wireless sensor scheduling in cyber–physical systems}, volume={113},
    DOI={<a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>},
    number={108759}, journal={Automatica}, publisher={Elsevier BV}, author={Leong,
    Alex S. and Ramaswamy, Arunselvan and Quevedo, Daniel E. and Karl, Holger and
    Shi, Ling}, year={2019} }'
  chicago: Leong, Alex S., Arunselvan Ramaswamy, Daniel E. Quevedo, Holger Karl, and
    Ling Shi. “Deep Reinforcement Learning for Wireless Sensor Scheduling in Cyber–Physical
    Systems.” <i>Automatica</i> 113 (2019). <a href="https://doi.org/10.1016/j.automatica.2019.108759">https://doi.org/10.1016/j.automatica.2019.108759</a>.
  ieee: 'A. S. Leong, A. Ramaswamy, D. E. Quevedo, H. Karl, and L. Shi, “Deep reinforcement
    learning for wireless sensor scheduling in cyber–physical systems,” <i>Automatica</i>,
    vol. 113, Art. no. 108759, 2019, doi: <a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>.'
  mla: Leong, Alex S., et al. “Deep Reinforcement Learning for Wireless Sensor Scheduling
    in Cyber–Physical Systems.” <i>Automatica</i>, vol. 113, 108759, Elsevier BV,
    2019, doi:<a href="https://doi.org/10.1016/j.automatica.2019.108759">10.1016/j.automatica.2019.108759</a>.
  short: A.S. Leong, A. Ramaswamy, D.E. Quevedo, H. Karl, L. Shi, Automatica 113 (2019).
date_created: 2023-01-09T16:44:58Z
date_updated: 2023-01-09T16:45:15Z
department:
- _id: '57'
doi: 10.1016/j.automatica.2019.108759
intvolume: '       113'
keyword:
- Electrical and Electronic Engineering
- Control and Systems Engineering
language:
- iso: eng
publication: Automatica
publication_identifier:
  issn:
  - 0005-1098
publication_status: published
publisher: Elsevier BV
status: public
title: Deep reinforcement learning for wireless sensor scheduling in cyber–physical
  systems
type: journal_article
user_id: '158'
volume: 113
year: '2019'
...
---
_id: '35584'
article_number: '108680'
author:
- first_name: Kemi
  full_name: Ding, Kemi
  last_name: Ding
- first_name: Xiaoqiang
  full_name: Ren, Xiaoqiang
  last_name: Ren
- first_name: Daniel E.
  full_name: Quevedo, Daniel E.
  last_name: Quevedo
- first_name: Subhrakanti
  full_name: Dey, Subhrakanti
  last_name: Dey
- first_name: Ling
  full_name: Shi, Ling
  last_name: Shi
citation:
  ama: Ding K, Ren X, Quevedo DE, Dey S, Shi L. Defensive deception against reactive
    jamming attacks in remote state estimation. <i>Automatica</i>. 2019;113. doi:<a
    href="https://doi.org/10.1016/j.automatica.2019.108680">10.1016/j.automatica.2019.108680</a>
  apa: Ding, K., Ren, X., Quevedo, D. E., Dey, S., &#38; Shi, L. (2019). Defensive
    deception against reactive jamming attacks in remote state estimation. <i>Automatica</i>,
    <i>113</i>, Article 108680. <a href="https://doi.org/10.1016/j.automatica.2019.108680">https://doi.org/10.1016/j.automatica.2019.108680</a>
  bibtex: '@article{Ding_Ren_Quevedo_Dey_Shi_2019, title={Defensive deception against
    reactive jamming attacks in remote state estimation}, volume={113}, DOI={<a href="https://doi.org/10.1016/j.automatica.2019.108680">10.1016/j.automatica.2019.108680</a>},
    number={108680}, journal={Automatica}, publisher={Elsevier BV}, author={Ding,
    Kemi and Ren, Xiaoqiang and Quevedo, Daniel E. and Dey, Subhrakanti and Shi, Ling},
    year={2019} }'
  chicago: Ding, Kemi, Xiaoqiang Ren, Daniel E. Quevedo, Subhrakanti Dey, and Ling
    Shi. “Defensive Deception against Reactive Jamming Attacks in Remote State Estimation.”
    <i>Automatica</i> 113 (2019). <a href="https://doi.org/10.1016/j.automatica.2019.108680">https://doi.org/10.1016/j.automatica.2019.108680</a>.
  ieee: 'K. Ding, X. Ren, D. E. Quevedo, S. Dey, and L. Shi, “Defensive deception
    against reactive jamming attacks in remote state estimation,” <i>Automatica</i>,
    vol. 113, Art. no. 108680, 2019, doi: <a href="https://doi.org/10.1016/j.automatica.2019.108680">10.1016/j.automatica.2019.108680</a>.'
  mla: Ding, Kemi, et al. “Defensive Deception against Reactive Jamming Attacks in
    Remote State Estimation.” <i>Automatica</i>, vol. 113, 108680, Elsevier BV, 2019,
    doi:<a href="https://doi.org/10.1016/j.automatica.2019.108680">10.1016/j.automatica.2019.108680</a>.
  short: K. Ding, X. Ren, D.E. Quevedo, S. Dey, L. Shi, Automatica 113 (2019).
date_created: 2023-01-09T16:45:46Z
date_updated: 2023-01-09T16:45:59Z
department:
- _id: '57'
doi: 10.1016/j.automatica.2019.108680
intvolume: '       113'
keyword:
- Electrical and Electronic Engineering
- Control and Systems Engineering
language:
- iso: eng
publication: Automatica
publication_identifier:
  issn:
  - 0005-1098
publication_status: published
publisher: Elsevier BV
status: public
title: Defensive deception against reactive jamming attacks in remote state estimation
type: journal_article
user_id: '158'
volume: 113
year: '2019'
...