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Information × Registration Number 0221U106512, 0121U112524 , R & D reports Title Resistance and robustness to perturbations of attractors of nonlinear infinite-dimensional systems popup.stage_title Head Kapustian Oleksii V., Доктор фізико-математичних наук Registration Date 09-12-2021 Organization Taras Shevchenko National University of Kyiv popup.description2  Object of study: attractors and approximate controls in systems with perturbations. Objective: to study the stability and robustness of global attractors and to construct approximate controls for infinite-dimensional evolutionary systems with respect to impulse and external perturbations. Research methods: results of the theory of nonlinear boundary value problems, theory of global attractors of infinite-dimensional dynamical systems, stability theory of dynamical systems, qualitative theory of impulse and stochastic systems, methods of nonlinear and multivalued analysis, averaging theory, stability theory. The stability and robustness of attracting sets and attractors, as well as the construction of effective approximate controls in nonlinear infinite-dimensional systems operating under the action of perturbations are studied. A qualitative theory of uniform attracting sets has been developed for impulse-perturbed systems. Under the most general conditions, the input data established effective sufficient conditions for the existence, stability and robustness of uniform attractors for asymptotically compact pulse processes generated by nonlinear wave equations with pulse perturbation, and the results of the existence and stability of uniform attractors for multivalued compact pulses. evolutionary systems such as reaction-diffusion. For evolutionary controlled systems with perturbations in the coefficients, the methods of constructing approximate optimal controls and approximate synthesis are substantiated. For nonlinear infinite-dimensional systems, the results on resistance to external perturbations were established. The input-state local stability (LISS) and asymptotic gain (AG) theorems for compact and asymptotically compact perturbed infinite-dimensional perturbed systems have been proved. The obtained theorems were applied to perturbed nonlinear wave equations, reaction-diffusion parabolic systems, and coupled PDE-ODE systems. Product Description popup.authors Zhuk Tetyana Yu. Kapustyan Olena A. Perestyuk Yuri М. Stanzhytsʹkyy Oleksandr М. popup.nrat_date 2021-12-09 Close