On Almost Periodic Trajectories of Control Systems with Feedback in the Form of Sweeping Processes

In the present paper, we consider a control system with feedback in the form of sweeping processes in Hilbert spaces. Using the notion of generalized metric space and A. I. Perov’s contraction mapping principle, we present a theorem on the existence and uniqueness of an almost periodic solution of t...

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Bibliographic Details
Published in:	Mathematical Notes Vol. 114; no. 1-2; pp. 85 - 91
Main Authors:	Kamenskii, M. I., Obukhovskii, V. V., Petrosyan, G. G.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-08-2023
Subjects:	14/34 639/766/189 639/766/530 639/766/747 Mathematics Mathematics and Statistics almost periodic function differential equation sweeping process generalized contraction operator differential inclusion generalized metric space exponentially stable matrix control system
Online Access:	Get full text
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Summary:	In the present paper, we consider a control system with feedback in the form of sweeping processes in Hilbert spaces. Using the notion of generalized metric space and A. I. Perov’s contraction mapping principle, we present a theorem on the existence and uniqueness of an almost periodic solution of this system and justify the application of the averaging principle to systems of this kind.
ISSN:	0001-4346 1573-8876
DOI:	10.1134/S0001434623070088