CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

Iryna Svyatovets

Abstract


The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts.

To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations.

A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation.

An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

Keywords


minimax control; almost conservative system; Riccati equation; small parameter; non-negative definite matrix

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DOI: http://dx.doi.org/10.21303/2461-4262.2017.00301

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