This article is cited in 1 paper

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

M. I. Kamenskii^a, V. V. Obukhovskii^b, G. Petrosyan<sup>b

a</sup> Voronezh State University
^b Voronezh State Pedagogical University

Abstract: 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.

Keywords: differential equation, control system, differential inclusion, sweeping process, almost periodic function, generalized metric space, generalized contraction operator, exponentially stable matrix.

UDC: 517.928

MSC: 34A60; 34C27; 34C29

Received: 15.02.2023

DOI: 10.4213/mzm13925

 English version: Mathematical Notes, 2023, 114:1, 85–91

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