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.