A Generalized Proportional Caputo Fractional Model of Multi-Agent Linear Dynamic Systems Via Impulsive Control Protocol


This paper deals with multi-agent systems that, due to using the generalized proportional Caputo fractional derivative, possess memories. The information exchange between agents does not occur continuously but only at fixed given update times, and the lower limit of the fractional derivative changes according to the update times. Two types of multi-agent systems are studied, namely systems without a leader and systems with a leader. For a generalized proportional Caputo fractional model of multi-agent linear dynamic systems, sufficient conditions for exponential stability via impulsive control are obtained. In the case of the presence of a leader in the multi-agent system, we derive sufficient conditions for the leader-following consensus via impulsive control based on the leader's influence. Simulation results are provided to verify the essential role of the generalized proportional Caputo fractional derivative and impulsive control in realizing the consensus of multi-agent systems.


Mathematics and Statistics


S. Hristova was supported by the Bulgarian Science Fund No. KP06N32/7. M. L. Morgado acknowledges support by the Fundação para a Ciência e Tecnologia within projects UIDB/04621/2020 and UIDP/04621/2020. A. B. Malinowska was supported by a Bialystok University by the Bialystok University of Technology Grant, financed from a subsidy provided by the Minister of Education and Science. R. Almeida is 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.

Keywords and Phrases

Consensus; Generalized Proportional Caputo Fractional Derivative; Impulsive Control; Leader; Multi-Agent Systems

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Article - Journal

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Publication Date

01 Dec 2022