Archives of Control Sciences

Almeida, Ricardo; Kamocki, Rafał; Malinowska, Agnieszka B.; Odzijewicz, Tatiana

doi:10.24425/acs.2020.135844

2020

DOI: 10.24425/acs.2020.135844

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Archives of Control Sciences

Ricardo Almeida,

Rafał Kamocki,

Agnieszka B. Malinowska

et al.

Abstract: 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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2024

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Cited by 2 publications

References 33 publications

(46 reference statements)

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A fuzzy q-closest alignment model

Mucha,

Peszek

2024

Nonlinearity

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The paper examines the issue of well-posedness of the Cucker-Smale model with communication restricted to the q-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy q-closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.

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A fuzzy q-closest alignment model

Mucha,

Peszek

2024

Nonlinearity

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On the multi-cluster flocking of the fractional Cucker–Smale model

Ahn

2024

MINE

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<p>This paper demonstrates several sufficient frameworks for the multi-cluster flocking behavior of the fractional Cucker–Smale (CS) model. For this, we first employ the Caputo fractional derivative instead of the usual derivative to propose the fractional CS model with the memory effect. Then, using mathematical tools based on fractional calculus, we present suitable sufficient conditions in terms of properly separated initial data close to the multi-cluster, and well-prepared system parameters for the multi-cluster flocking of the fractional system to emerge. Finally, we offer several numerical simulations and compare them with the analytical results.</p>

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Archives of Control Sciences

Cited by 2 publications

References 33 publications

A fuzzy q-closest alignment model

A fuzzy q-closest alignment model

On the multi-cluster flocking of the fractional Cucker–Smale model

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