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Visn. Nac. Akad. Nauk Ukr. 2020. (1): 29-37
https://doi.org/10.15407/visn2020.01.029

A.L. Zuyev
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Sloviansk
ORCID: http://orcid.org/0000-0002-7610-5621

MATHEMATICAL CONTROL THEORY: NONLINEAR DYNAMICS AND ENGINEERING APPLICATIONS
According to the materials of scientific report at the meeting of the Presidium of NAS of Ukraine, November 6, 2019

One of the most important tasks in mathematical control theory is to stabilize unstable dynamic processes by applying a feedback law. The report introduces a new approach for solving the stabilization problem, which makes it possible to effectively define control strategies for a wide class of essentially nonlinear controlled dynamical systems. The class of systems under investigation includes, in particular, mathematical models in robotics and controlled engineering structures with elastic beams, plates, and shells. The obtained theoretical results are applied to problems of stabilization and navigation of mobile robots in environments with obstacles. Computer simulation results are also presented to illustrate the vibrations of a controlled shell, which is used for experiments with novel lightweight elastic structures in civil engineering. A part of this report is devoted to the application of methods of mathematical control theory to the optimization of processes in chemical engineering in the sense of minimizing the consumption of input reactants (raw materials) or maximizing the productivity. For this purpose, a class of isoperimetric optimal control problems for non-stationary mass and energy balance equations has been solved in order to improve the performance of chemical reactors in comparison to their steady-state operation.
Keywords: mathematical control theory, stabilization of motion, motion planning in robotics, optimization of chemical reactions.

Language of article: ukrainian

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