IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i24p3981-d1546811.html
   My bibliography  Save this article

Optimal Control of a Harmonic Oscillator with Parametric Excitation

Author

Listed:
  • Dmitrii Kamzolkin

    (Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China
    These authors contributed equally to this work.)

  • Victor Ilyutko

    (Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China
    These authors contributed equally to this work.)

  • Vladimir Ternovski

    (Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, International University Park Road 1, Shenzhen 518172, China
    These authors contributed equally to this work.)

Abstract

This paper addresses the time-optimal control problem for a harmonic oscillator characterized by a time-dependent frequency. The primary objective is to determine the minimal time required to transition the system from an initial state, defined by a given position and velocity, to a specified final state, while ensuring that the frequency remains within prescribed bounds. The key challenge lies in identifying the optimal switching times between two available frequencies to meet all boundary conditions efficiently. By examining various boundary scenarios, constructing the reachable set of all admissible trajectories, and employing both analytical techniques and control theory, we develop a robust solution strategy. This work holds particular relevance for practical applications demanding rapid state transitions, such as mechanical vibration control and signal processing, where achieving time-optimal performance is critical. Furthermore, the methods presented are adaptable to a wide range of systems facing similar constraints, providing a versatile and effective framework for time-optimal control.

Suggested Citation

  • Dmitrii Kamzolkin & Victor Ilyutko & Vladimir Ternovski, 2024. "Optimal Control of a Harmonic Oscillator with Parametric Excitation," Mathematics, MDPI, vol. 12(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3981-:d:1546811
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/24/3981/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/24/3981/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Vladimir Ternovski & Victor Ilyutko, 2024. "Control the Coefficient of a Differential Equation as an Inverse Problem in Time," Mathematics, MDPI, vol. 12(2), pages 1-16, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jianwen Ren & Yingqiang Xu & Shiyuan Wang, 2018. "A Distributed Robust Dispatch Approach for Interconnected Systems with a High Proportion of Wind Power Penetration," Energies, MDPI, vol. 11(4), pages 1-18, April.
    2. Li, Xingchen & Xu, Guangcheng & Wu, Jie & Xu, Chengzhen & Zhu, Qingyuan, 2024. "Evaluation of bank efficiency by considering the uncertainty of nonperforming loans," Omega, Elsevier, vol. 126(C).
    3. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    4. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    5. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    6. Sarhadi, Hassan & Naoum-Sawaya, Joe & Verma, Manish, 2020. "A robust optimization approach to locating and stockpiling marine oil-spill response facilities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    7. Li, Shukai & Liu, Ronghui & Yang, Lixing & Gao, Ziyou, 2019. "Robust dynamic bus controls considering delay disturbances and passenger demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 88-109.
    8. Jeong, Jaehee & Premsankar, Gopika & Ghaddar, Bissan & Tarkoma, Sasu, 2024. "A robust optimization approach for placement of applications in edge computing considering latency uncertainty," Omega, Elsevier, vol. 126(C).
    9. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    10. Akhtar Hussain & Van-Hai Bui & Hak-Man Kim, 2016. "Robust Optimization-Based Scheduling of Multi-Microgrids Considering Uncertainties," Energies, MDPI, vol. 9(4), pages 1-21, April.
    11. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    12. Kandpal, Bakul & Pareek, Parikshit & Verma, Ashu, 2022. "A robust day-ahead scheduling strategy for EV charging stations in unbalanced distribution grid," Energy, Elsevier, vol. 249(C).
    13. Jun-ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2020. "Worst-case sensitivity," Papers 2010.10794, arXiv.org.
    14. Guo, Shiliang & Li, Pengpeng & Ma, Kai & Yang, Bo & Yang, Jie, 2022. "Robust energy management for industrial microgrid considering charging and discharging pressure of electric vehicles," Applied Energy, Elsevier, vol. 325(C).
    15. Zhang, Hanxiao & Li, Yan-Fu, 2022. "Robust optimization on redundancy allocation problems in multi-state and continuous-state series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    16. Evers, L. & Dollevoet, T.A.B. & Barros, A.I. & Monsuur, H., 2011. "Robust UAV Mission Planning," Econometric Institute Research Papers EI 2011-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Shen, Feifei & Zhao, Liang & Wang, Meihong & Du, Wenli & Qian, Feng, 2022. "Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty," Applied Energy, Elsevier, vol. 307(C).
    18. Baringo, Luis & Boffino, Luigi & Oggioni, Giorgia, 2020. "Robust expansion planning of a distribution system with electric vehicles, storage and renewable units," Applied Energy, Elsevier, vol. 265(C).
    19. Mohammad Reza Ghatreh Samani & Seyyed-Mahdi Hosseini-Motlagh, 2021. "A robust framework for designing blood network in disaster relief: a real-life case," Operational Research, Springer, vol. 21(3), pages 1529-1568, September.
    20. Thomas Schmitt & Tobias Rodemann & Jürgen Adamy, 2021. "The Cost of Photovoltaic Forecasting Errors in Microgrid Control with Peak Pricing," Energies, MDPI, vol. 14(9), pages 1-13, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3981-:d:1546811. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.