On almost periodic trajectories of control systems with feedback in the form of sweeping processes (Q6063067)

Existence and uniqueness of an almost periodic solution is proven for a system of differential equations with feedback control in Hilbert space where the derivatives of the controls \(u_j'\) are assumed to satisfy an inclusion involving the moving set \(N_{C_j(t)} \left(u_j(t) \right)\), where \(C_j\) is \(r\)-proximally regular, Lipschitz and compact-valued. An averaging principle is also proven. The proofs use a fixed point theorem from [\textit{A. I. Perov}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2005, No. 1, 196--207 (2005; Zbl 1161.54307)] and also [\textit{M. Kamenskii} and \textit{P. Nistri}, Set-Valued Anal. 11, No. 4, 345--357 (2003; Zbl 1034.34075)].