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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
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    References listed on IDEAS

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    1. Sergio Adriani David & Carlos Alberto Valentim, 2015. "Fractional Euler-Lagrange Equations Applied to Oscillatory Systems," Mathematics, MDPI, vol. 3(2), pages 1-15, April.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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 3.
    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 1.
    10. 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.
    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. 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.
    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. 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.
    15. 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.
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    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.

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