Optimal control of the discrete-time fractional-order Cucker-Smale model

Agnieszka B. Malinowska; Tatiana Odzijewicz

doi:10.3934/dcdsb.2018023

Article Contents

2018, Volume 23, Issue 1: 347-357. Doi: 10.3934/dcdsb.2018023

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Optimal control of the discrete-time fractional-order Cucker-Smale model

Agnieszka B. Malinowska^1, , and
Tatiana Odzijewicz^2,

1.
Faculty of Computer Science, Bialystok University of Technology, 15-351 Bia lystok, Poland
2.
Department of Mathematics and Mathematical Economics, Warsaw School of Economics, 02-554 Warsaw, Poland

* Corresponding author: a.malinowska@pb.edu.pl
* Corresponding author: a.malinowska@pb.edu.pl

Received: August 31, 2016

Revised: October 31, 2016

Published: November 2017

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Abstract

We obtain necessary optimality conditions for the discrete-time fractional-order Cucker-Smale optimal control problem. By using fractional order differences on the left side of nonlinear system we introduce memory effects to the considered problem.

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Mathematics Subject Classification: Primary: 49K99, 26A33; Secondary: 39A99, 90C25.

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Figure 1. Consensus parameters with using control

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Figure 2. Consensus parameters without control

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