IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v5y2017i2p25-d96239.html
   My bibliography  Save this article

Discrete-Time Fractional Optimal Control

Author

Listed:
  • Tirumalasetty Chiranjeevi

    (Department of Electrical Engineering, National Institute of Technology, Silchar 788010, Assam, India)

  • Raj Kumar Biswas

    (Department of Electrical Engineering, National Institute of Technology, Silchar 788010, Assam, India)

Abstract

A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples are taken up and their solution technique is presented. Results are produced for different values of α .

Suggested Citation

  • Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:25-:d:96239
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/5/2/25/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/5/2/25/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tian Liang Guo, 2013. "The Necessary Conditions of Fractional Optimal Control in the Sense of Caputo," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 115-126, January.
    2. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    3. Sergio Adriani David & Carlos Alberto Valentim, 2015. "Fractional Euler-Lagrange Equations Applied to Oscillatory Systems," Mathematics, MDPI, vol. 3(2), pages 1-15, April.
    4. José Paulo Carvalho dos Santos & Lislaine Cristina Cardoso & Evandro Monteiro & Nelson H. T. Lemes, 2015. "A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-10, July.
    5. Hamed Al-Sulami & Moustafa El-Shahed & Juan J. Nieto & Wafa Shammakh, 2014. "On Fractional Order Dengue Epidemic Model," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, August.
    6. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    7. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    8. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    10. Sierociuk, Dominik & Skovranek, Tomas & Macias, Michal & Podlubny, Igor & Petras, Ivo & Dzielinski, Andrzej & Ziubinski, Pawel, 2015. "Diffusion process modeling by using fractional-order models," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 2-11.
    11. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    12. Angstmann, C.N. & Henry, B.I. & McGann, A.V., 2016. "A fractional-order infectivity SIR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 86-93.
    13. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    14. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
    15. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raul Nistal & Manuel De la Sen & Santiago Alonso-Quesada & Asier Ibeas, 2018. "On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties," Mathematics, MDPI, vol. 7(1), pages 1-19, December.
    2. Arindita Saha & Puja Dash & Naladi Ram Babu & Tirumalasetty Chiranjeevi & Bathina Venkateswararao & Łukasz Knypiński, 2022. "Impact of Spotted Hyena Optimized Cascade Controller in Load Frequency Control of Wave-Solar-Double Compensated Capacitive Energy Storage Based Interconnected Power System," Energies, MDPI, vol. 15(19), pages 1-25, September.
    3. Meriem Boukhobza & Amar Debbouche & Lingeshwaran Shangerganesh & Juan J. Nieto, 2024. "The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time," Mathematics, MDPI, vol. 12(8), pages 1-24, April.

    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. Kritana Prueksakorn & Cheng-Xu Piao & Hyunchul Ha & Taehyeung Kim, 2015. "Computational and Experimental Investigation for an Optimal Design of Industrial Windows to Allow Natural Ventilation during Wind-Driven Rain," Sustainability, MDPI, vol. 7(8), pages 1-22, August.
    2. Hualin Xie & Jinlang Zou & Hailing Jiang & Ning Zhang & Yongrok Choi, 2014. "Spatiotemporal Pattern and Driving Forces of Arable Land-Use Intensity in China: Toward Sustainable Land Management Using Emergy Analysis," Sustainability, MDPI, vol. 6(6), pages 1-17, May.
    3. Stephan E. Maurer & Andrei V. Potlogea, 2021. "Male‐biased Demand Shocks and Women's Labour Force Participation: Evidence from Large Oil Field Discoveries," Economica, London School of Economics and Political Science, vol. 88(349), pages 167-188, January.
    4. Tie Hua Zhou & Ling Wang & Keun Ho Ryu, 2015. "Supporting Keyword Search for Image Retrieval with Integration of Probabilistic Annotation," Sustainability, MDPI, vol. 7(5), pages 1-18, May.
    5. T. Karski, 2019. "Opinions and Controversies in Problem of The So-Called Idiopathic Scoliosis. Information About Etiology, New Classification and New Therapy," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 12(5), pages 9612-9616, January.
    6. Wesley Mendes-da-Silva, 2020. "What Makes an Article be More Cited?," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 24(6), pages 507-513.
    7. Wisdom Akpalu & Mintewab Bezabih, 2015. "Tenure Insecurity, Climate Variability and Renting out Decisions among Female Small-Holder Farmers in Ethiopia," Sustainability, MDPI, vol. 7(6), pages 1-16, June.
    8. Wei Chen & Shu-Yu Liu & Chih-Han Chen & Yi-Shan Lee, 2011. "Bounded Memory, Inertia, Sampling and Weighting Model for Market Entry Games," Games, MDPI, vol. 2(1), pages 1-13, March.
    9. David Harborth & Sebastian Pape, 2020. "Empirically Investigating Extraneous Influences on the “APCO” Model—Childhood Brand Nostalgia and the Positivity Bias," Future Internet, MDPI, vol. 12(12), pages 1-16, December.
    10. Taeyeoun Roh & Yujin Jeong & Byungun Yoon, 2017. "Developing a Methodology of Structuring and Layering Technological Information in Patent Documents through Natural Language Processing," Sustainability, MDPI, vol. 9(11), pages 1-19, November.
    11. He-Yau Kang & Amy H. I. Lee & Tzu-Ting Huang, 2016. "Project Management for a Wind Turbine Construction by Applying Fuzzy Multiple Objective Linear Programming Models," Energies, MDPI, vol. 9(12), pages 1-15, December.
    12. A. B. Atkinson & Stephen P. Jenkins, 2020. "A Different Perspective on the Evolution of UK Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(2), pages 253-266, June.
    13. Haiyan Xu & Yanhui Ding & Jing Sun & Kun Zhao & Yuanjian Chen, 2019. "Dynamic Group Recommendation Based on the Attention Mechanism," Future Internet, MDPI, vol. 11(9), pages 1-15, September.
    14. Adina Letiţia Negruşa & Valentin Toader & Aurelian Sofică & Mihaela Filofteia Tutunea & Rozalia Veronica Rus, 2015. "Exploring Gamification Techniques and Applications for Sustainable Tourism," Sustainability, MDPI, vol. 7(8), pages 1-30, August.
    15. Ahmad N. Alkenani & Mohammad Ashraf & Ghulam Mohammad, 2020. "Quantum Codes from Constacyclic Codes over the Ring F q [ u 1 , u 2 ]/〈 u 1 2 - u 1 , u 2 2 - u 2 , u 1 u 2 - u 2 u 1 〉," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    16. Shang-Yuan Chen & Jui-Ting Huang, 2012. "A Smart Green Building: An Environmental Health Control Design," Energies, MDPI, vol. 5(5), pages 1-16, May.
    17. Yanhong Feng & Xu Yu & Gai-Ge Wang, 2019. "A Novel Monarch Butterfly Optimization with Global Position Updating Operator for Large-Scale 0-1 Knapsack Problems," Mathematics, MDPI, vol. 7(11), pages 1-31, November.
    18. Xiaoshu Cao & Feiwen Liang & Huiling Chen & Yongwei Liu, 2017. "Circuity Characteristics of Urban Travel Based on GPS Data: A Case Study of Guangzhou," Sustainability, MDPI, vol. 9(11), pages 1-21, November.
    19. S. B. Reshetnikov & M. R. Skirdov, 2017. "Analysis of methodological approaches to determination and assessment of the human capital," Russian Journal of Industrial Economics, MISIS, vol. 10(1).
    20. Mi Jung Son & Jin Han Park & Ka Hyun Ko, 2019. "Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making," Mathematics, MDPI, vol. 7(7), pages 1-33, July.

    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:5:y:2017:i:2:p:25-:d:96239. 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.