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Information × Registration Number 0203U008081, 0100U003352 , R & D reports Title Non -linear dynamical systems and control popup.stage_title Head Korobov V., Registration Date 22-04-2003 Organization Kharkov National University named after V.N.Karazin popup.description2 The object of investigation are control systems of differenttial equations, control systems of integro-differential equations, control processes described by linear and nonlinear equation in Hilbert space. The aim of the research is to obtain conditions for solvability of the positional synthesis problem with constraints on control and its derivatives, to obtain conditions for global controllability for triangular integro-differential systems, to construct the set of positional controls satisfying the given constraints for the control processes described by linear and nonlinear equation in Hilbert space. The method of research is successive analytic and logic analysis of the investigated objects. The method of controllability function is extended on the positional synthesis problems with constraints on control and its derivatives. For linear system the family of positional controls is selected. Every control from family solves the local positional synthesis problem of inertial controls. In the limit case the corresponding control solves the stabilisation problem. For nonlinear system with the one-dimensional control the mentioned problem is solved by the first approximation. For the control processes descibed by linear equation with bounded operator in Hilbert space the set of the positional controls satisfying the given constraints has been constructed. The local synthesis problem has been solved for the equations with the bounded operator. In the case of the ajoint operator the global synthesis problem has been solved. For the nonlinear equation the local synthesis problem has been solved by the first approximation. The local synthesis problem has been solved for the linear unbounded operator having the ortogonal normed basis consisting from the eigenvectors. The significance of the research is defined by the possibility to apply its results to the various problems such as the optimal synthesis problem, the problems of stabilisation, controllability, identification. The prediction is to fine new effective methods to construct the positional control with constraints on its derivatives, to fined effective methods to construct controls providing the property of global controllability. Product Description popup.authors popup.nrat_date 2020-04-02 Close