Optimal control of discrete-time fractional multi-agent systems
type: Item
instance of: scholarly article
title: Optimal control of discrete-time fractional multi-agent systems
zbMATH Open document ID: 1392.49032
author: Agnieszka B. Malinowska
author: Tatiana Odzijewicz
published in: Journal of Computational and Applied Mathematics
publication date: 2018-05-09T00:00:00Z
review text: The authors consider optimal control problems for discrete-time multi-agents systems. The systems are described by fractional difference equations in two variants. In the first variant each agent is described by time-dependent consensus parameter and external control strategies. The objective is to minimize control and disagreements among agents. In the second variant each agent is represented by two coordinates representing the time-dependent state and consensus parameters, and the objective is to minimize control inputs together with the distance among agents and discrepancy of the consensus variables to the mean of those variables. The performance indices are quadratic functions of state and control variables. Basing on the theory of extremal smooth-convex problems [\textit{A. D. Ioffe} and \textit{V. M. Tihomirov}, Theory of extremal problems. Translated from the Russian by K. Makowski. New York, Oxford: North-Holland Publishing Company (1979; Zbl 0407.90051)] the authors formulate necessary conditions of optimality for two optimization problems mentioned above. The idea is to convert the optimal control problems into finite dimensional optimization problem and use the relative extremum principle. To illustrate proposed methodology three numerical (academic) examples are presented.
Mathematics Subject Classification ID: 49K30
Mathematics Subject Classification ID: 68T42
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 6867157
zbMATH Keywords: fractional discrete time systems
zbMATH Keywords: optimal control
zbMATH Keywords: multi-agent systems
zbMATH Keywords: convex problems
zbMATH Keywords: emergent behavior
reviewed by: Andrzej Świerniak
MaRDI profile type: Publication
full work available at URL: j.cam.2017.10.014
OpenAlex ID: W2765600789
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DOI: 10.1016/J.CAM.2017.10.014
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description: scientific article; zbMATH DE number 6867157