Geodesic
On Almost Periodic Trajectories of Control Systems with Feedback in the Form of Sweeping Processes
Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 104-112

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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. 
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     title = {On {Almost} {Periodic} {Trajectories} of {Control} {Systems} with {Feedback} in the {Form} of {Sweeping} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
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M. I. Kamenskii; V. V. Obukhovskii; G. Petrosyan. On Almost Periodic Trajectories of Control Systems with Feedback in the Form of Sweeping Processes. Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 104-112. http://geodesic.mathdoc.fr/item/MZM_2023_114_1_a7/