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http://hdl.handle.net/10773/29593
Title: | Distributed-order non-local optimal control |
Author: | Ndaïrou, Faïçal Torres, Delfim F. M. |
Keywords: | Distributed-order fractional calculus Basic optimal control problem Pontryagin extremals |
Issue Date: | Dec-2020 |
Publisher: | MDPI |
Abstract: | Distributed-order fractional non-local operators were introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted integral of different orders of differentiation over a certain range. The subject of distributed-order non-local derivatives is currently under strong development due to its applications in modeling some complex real world phenomena. Fractional optimal control theory deals with the optimization of a performance index functional, subject to a fractional control system. One of the most important results in classical and fractional optimal control is the Pontryagin Maximum Principle, which gives a necessary optimality condition that every solution to the optimization problem must verify. In our work, we extend the fractional optimal control theory by considering dynamical system constraints depending on distributed-order fractional derivatives. Precisely, we prove a weak version of Pontryagin’s maximum principle and a sufficient optimality condition under appropriate convexity assumptions. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/29593 |
DOI: | 10.3390/axioms9040124 |
ISSN: | 2075-1680 |
Publisher Version: | https://www.mdpi.com/2075-1680/9/4/124 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[467]Ndairou_Torres-axioms.pdf | 268.47 kB | Adobe PDF | View/Open |
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