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Information × Registration Number 0219U102049, 0119U103214 , R & D reports Title Stabilization of trajectories of dynamical systems with hybrid controls and approximation of solutions to non-autonomous boundary value problems. popup.stage_title Head Zuev Olexandr L., Доктор фізико-математичних наук Registration Date 16-12-2019 Organization Інститут прикладної математики і механіки НАН України popup.description2  A new method of constructing control functions that stabilize the equilibrium of a class of systems whose vector fields satisfy certain commuting properties is proposed. This method is applied to the stabilization problem of the Euler equations of rotational motion of a rigid body with two actuators. For this nonlinear system, a family of time-varying feedback controls has been constructed. Nonlinear mechanical systems which do not satisfy Brockett's necessary stabilizability condition are investigated. Algorithms for control design with the use of random processes that ensure the asymptotic stability of equilibrium of such systems are proposed. A numerical scheme is developed for approximate computing of the eigenfrequencies for a mechanical system consisting of an elastic beam with an attached mass, taking into account the stiffness and inertial parameters. An approximate frequency equation is constructed for the asymptotic estimation of the eigenvalues of the considered spectral problem. The non-critical and critical cases of a nonlinear boundary value problem for a non-degenerate differential-algebraic system are investigated. Sufficient conditions for the existence of a solution to the nonlinear Noetherian boundary value problem in the non-critical case and the conditions for the reducibility of the critical case to non-critical are obtained. Product Description popup.authors Vasylieva Iryna H. Hrushkovska Viktoriia V. Kalosha Julia I. Nesmelova Olga V. Novikova Yuliia V. popup.nrat_date 2020-04-02 Close