Distributed-Order Non-Local Optimal Control

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 rang...

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Veröffentlicht in:Axioms 2020-12, Vol.9 (4), p.124
Hauptverfasser: Ndaïrou, Faïçal, Torres, Delfim F. M.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms9040124