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...

Full description

Saved in:
Bibliographic Details
Published inAxioms Vol. 9; no. 4; p. 124
Main Authors Ndaïrou, Faïçal, Torres, Delfim F. M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2020
Subjects
Control systems
Control theory
Convexity
Derivatives
Indexing
Inequality
Integrals
Mathematical functions
Maximum principle
Operators (mathematics)
Optimal control
Optimization
Performance indices
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms9040124