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Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems

Author

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  • Touria Karite

    (Laboratory of Engineering, Systems and Applications, Department of Electrical Engineering & Computer Science, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Avenue My Abdallah Km 5 Route d’Imouzzer, Fez BP 72, Morocco
    These authors contributed equally to this work.)

  • Adil Khazari

    (Laboratory of Analysis, Mathematics and Applications, National School of Commerce & Management, Sidi Mohamed Ben Abdellah University, Fez BP 1796, Morocco
    These authors contributed equally to this work.)

  • Delfim F. M. Torres

    (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

Abstract

We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.

Suggested Citation

  • Touria Karite & Adil Khazari & Delfim F. M. Torres, 2022. "Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4813-:d:1007071
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    References listed on IDEAS

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    1. Ahmed M. Elshenhab & Xingtao Wang & Clemente Cesarano & Barakah Almarri & Osama Moaaz, 2022. "Finite-Time Stability Analysis of Fractional Delay Systems," Mathematics, MDPI, vol. 10(11), pages 1-11, May.
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