The existence of consensus of a leader-following problem with Caputo fractional derivative | Zendy

Ewa Schmeidel | Zendy

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The existence of consensus of a leader-following problem with Caputo fractional derivative

Author(s) -

Ewa Schmeidel

Publication year - 2018

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2019.39.1.77

Subject(s) - mathematics , resolvent , nonlinear system , trajectory , fixed point theorem , schauder fixed point theorem , consensus , fractional calculus , kernel (algebra) , mathematical analysis , pure mathematics , multi agent system , computer science , picard–lindelöf theorem , physics , quantum mechanics , astronomy , artificial intelligence

In this paper, consensus of a leader-following problem is investigated. The leader-following problem describes a dynamics of the leader and a number of agents. The trajectory of the leader is given. The dynamics of each agent depends on the leader trajectory and others agents' inputs. Here, the leader-following problem is modeled by a system of nonlinear equations with Caputo fractional derivative, which can be rewritten as a system of Volterra equations. The main tools in the investigation are the properties of the resolvent kernel corresponding to the Volterra equations, and Schauder fixed point theorem. By study of the existence of an asymptotically stable solution of a suitable Volterra system, the sufficient conditions for consensus of the leader-following problem are obtained.

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