scholarly journals Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory

2013 ◽  
Vol 3 (1) ◽  
pp. 161-173 ◽  
Author(s):  
Hans Josef Pesch ◽  
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Theory ◽  
Calculus Of Variations ◽  
Optimal Control Theory ◽  
The Maximum Principle ◽  
Royal Road

scholarly journals Distributed-Order Non-Local Optimal Control

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 124
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Theory ◽  
Optimality Condition ◽  
Optimal Control Theory ◽  
Sufficient Optimality Condition ◽  
Weak Version ◽  
Fractional Optimal Control ◽  
Non Local ◽  
Distributed Order

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.

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