A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem

Mathematics – Optimization and Control

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

24 pages

Scientific paper

In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional Pontryagin's system and the proof is based on the introduction of a Lagrange multiplier. Assuming an additional condition on these problems, we suggest a new presentation of this result with a proof using only classical mathematical tools adapted to the fractional case: calculus of variations, Gronwall's Lemma, Cauchy-Lipschitz Theorem and stability under perturbations of differential equations. In this paper, we furthermore provide a way in order to transit from a classical optimal control problem to its fractional version via the Stanislavsky's formalism. We also solve a strict fractional example allowing to test numerical schemes. Finally, we state a fractional Noether's theorem giving the existence of an explicit constant of motion for fractional Pontryagin's systems admitting a symmetry.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-393657

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.