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

Touria Karite, Adil Khazari and Delfim F. M. Torres ()
Additional contact information
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
Adil Khazari: Laboratory of Analysis, Mathematics and Applications, National School of Commerce & Management, Sidi Mohamed Ben Abdellah University, Fez BP 1796, Morocco
Delfim F. M. Torres: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2022, vol. 10, issue 24, 1-16

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.

Keywords: regional controllability; fractional-order systems; Caputo derivatives; control delays; optimal control; minimum energy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/24/4813/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/24/4813/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:24:p:4813-:d:1007071

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().