0214U007989, R & D reports
Solving the problems of controllability, linearization, synthesis and stabilization for nonlinear systems
Кorobov Valery, Доктор фізико-математичних наук
Kharkov National University named after V.N. Karazin
The objects of investigation are control systems of differential equations, algebraic systems of nonlinear equations. The aim of the research is obtaining of constructive solution for the admission positional synthesis problem for nonlinear control systems with discontinuous right-hand side; getting of the solution of the identification problem for linear non-stationary Boltzmann equation with diffused parameters and non-stationary unisotropic collisions integral in an arbitrary Euklid space; obtaining of the necessary and sufficient conditions for the robast stabilization of a class of nonlinear control systems; investigating of dynamic processes which are described by means of the systems of the ordinary differential equations and the systems with an one-dimensional control; solving the systems of nonlinear almost polynomial equations; investigating of the affine systems with multy-dimentional controls. Namely, development of analytical methods to solve the problems of controllability, of an admission synthesis of positional and inertial controls; finding the classes of the nonlinear systems with an one-dimensional control which are mapped on the simplest structure systems of the special form by means of the change of variables only, developing of the algorithm to construct such mappings; constructive solution of the controllability problem for such given nonlinear systems using the obtained results; constructing the numerical algorithms for solving the systems of nonlinear almost polynomial equations; solving the linearization, stabilization and synthesis of the bounded controls problems for the affine systems with multy-dimentional controls. The method of the research is successive analytic and logic analysis of the investigated objects. The significance of the research is defined by the theoretical and practical value of its results. The prediction is to find the effective analytic and numerical methods to construct the controls provided the 0-controllability, solving the synthesis and stabilization problems, searching the effective analytic and numerical methods to solve the systems of nonlinear almost polynomial equations.