On the existence of optimal consensus control for the fractional Cucker-Smale model

This paper addresses the nonlinear Cucker-Smale optimal control problem under the interplay of memory effect. The aforementioned effect is included by employing the Caputo fractional derivative in the equation representing the velocity of agents. Sufficient conditions for the existence of solutions to the considered problem are proved and the analysis of some particular problems is illustrated by two numerical examples.

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R. Almeida was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UIDB/04106/2020. A. B. Malinowska was supported by the Bialystok University of Technology Grant, financed from a subsidy provided by the Minister of Science and Higher Education and T. Odzijewicz by the SGH Warsaw School of Economics grant KAE/DB/20.