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Title: Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems
Authors: Gomoyunov, M. I.
Issue Date: 2018
Publisher: De Gruyter
Citation: Gomoyunov M. I. Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems / M. I. Gomoyunov. — DOI 10.1515/fca-2018-0066 // Fractional Calculus and Applied Analysis. — 2018. — Vol. 21. — Iss. 5. — P. 1238-1261.
Abstract: The paper is devoted to the development of control procedures with a guide for fractional order dynamical systems controlled under conditions of disturbances, uncertainties or counteractions. We consider a dynamical system which motion is described by ordinary fractional differential equations with the Caputo derivative of an order α ∈ (0, 1). For the case when the guide is, in a certain sense, a copy of the system, we propose a mutual aiming procedure between the original system and guide. The proof of proximity between motions of the systems is based on the estimate of the fractional derivative of the superposition of a convex Lyapunov function and a function represented by the fractional integral of an essentially bounded measurable function. This estimate can be considered as a generalization of the known estimates of such type. We give an example that illustrates the workability of the proposed control procedures with a guide. © 2018 Diogenes Co., Sofia.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85060782518
PURE ID: 8878005
ISSN: 13110454
DOI: 10.1515/fca-2018-0066
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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