ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Almost Periodic Solutions in Control Systems with Monotone Nonlinearities

Author(s):

Yuri Nikolaevich Kalinin

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
postgraduate student

shouganai@mail.ru

Volker Reitmann

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
professor of the Department of Applied Cybernetics
Prof. Dr.

vreitmann@aol.com

Abstract:

We investigate control systems as variational equations in non-standard chains of rigged Hilbert spaces. Monotonicity properties of nonlinearities are introduced with respect to such riggings generated by Lyapunov operators and invariant cones. Sufficient frequency domain conditions for boundedness and the existence of Bohr and Stepanov almost periodic solutions are derived. As an example we consider equations with Duffing-type nonlinearities and almost periodic forcing terms.

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