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Information × Registration Number 0216U002866, 0116U007761 , R & D reports Title Methods of synthesis of control functions for motion planning and stabilization problems of multi-frequency mechanical systems. popup.stage_title Head Grushkovska Victoria Vasylivna, Кандидат фізико-математичних наук Registration Date 19-12-2016 Organization Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine popup.description2 This project is devoted to the study of stabilization and motion planning for nonlinear multi-frequency systems. By using the Volterra series and an auxiliary Lie bracket system, we develop a new constructive method for motion planning in a neighborhood of a given curve for systems whose vector fields satisfy the Lie algebra rank condition. Besides, a gradient-free control functions are constructed for approximate trajectory tracking problem. By using the modification of the Lyapunov method, practical asymptotic stability property is proved for systems with obtained controls. A mathematical model of the mechanical system consisting of a rigid body and an isotropic plate is considered. The equation of the plate oscillations is approximated by a linear system in modal coordinates. The subsystem corresponding to the odd modes is represented in the operator form, and the controls stabilizing its zero equilibrium are obtained. The influence of the number of modes on the difference between the solutions of the system with obtained controls and a given state is also studied. The results obtained are illustrated with several examples. Product Description popup.authors Новікова Юлія Вікторівна popup.nrat_date 2020-04-02 Close