Svyatovets I. Research of controlled gyroscopic almost conservative systems

In the thesis the problem of control of dynamic systems is investigated. In particular, the problem of applying the feedback vector to construct continuous and discrete almost conservative systems is considered. The conditions for the existence of the desired control are investigated. For this, different approaches are used: the use of some skew-symmetric matrix to obtain the necessary condition; application of the Kronecker product of matrices. An approach is used in which the necessary matrix of coefficients is first constructed, and then the feedback vector is found. It shows how one can construct a control that simultaneously solves two problems: obtaining a nonsingular skew-symmetric matrix and, as a consequence, forming an almost conservative system and constructing an optimal control. The problem of constructing an almost conservative system is solved by methods of modal control, in which the desired location of the roots of the characteristic equation can be preset in advance. A step-by-step description of the application of modal control for a fourth-order system with a two-dimensional control vector and its generalization for a system of order 2n with an m-dimensional control vector is proposed. The problem of minimax control of almost conservative systems, on which there is an unknown perturbation with limited energy, is investigated. The criterion for estimating a parameter contained in the corresponding Riccati equation is formulated. Examples of corresponding mathematical models of gyroscopic systems are considered, which illustrate the approaches described for the formation of almost conservative systems by feedback.