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Information × Registration Number 0304U004086, 0103U004229 , R & D reports Title Mathematical theory of controlled systems popup.stage_title Позиційний синтез керувань з обмеженнями на керування та його похідні до заданого порядку для класів систем, які відображаються на лінійні Head Korobov V., Registration Date 20-03-2004 Organization Kharkov National University named after V.N.Karazin popup.description2 The objects of investigation are control systems of differential equations. The aim of the research is to obtain conditions for solvability of the positional synthesis problem with constraints on control and its derivatives, to construct the set of the positional controls satisfying the giving constraints and transforming an initial point to the origin at the finite time. The method of the 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 is selected. Every control from the family solves the local positional synthesis problem of inertial controls. In the limit case the corresponding control solves the stabilization problem. In addition the time of the motion is determined by means of the controllability function. For nonlinear system with the one-dimensional control the mentioned problem is solved by the first approximation. The upper estimate on the time of the motion is obtained. The triangular system (with the zero state point ) which can be mapping to the canonical system by means of the variable change and the additive control change are also considered. For these systems the controls solving the mentioned problem and satisfying with the first derivative the giving constraints are constructed as well. If the triangular system is mapping on the linear system by means of the variable change only then the family of controls are constructed. Each control from the family solves the positional synthesis problem and satisfies with the derivative of any order the giving constraints. The time of the motion and the corresponding trajectories are calculated as well. The significance of the research is defined by the possibility to apply its results to the various problems such as optimal control synthesis problem, stabilization problem. Product Description popup.authors popup.nrat_date 2020-04-02 Close