THE PROBLEM OF PARAMETRIC SYNTHESIS OF A CONTROL OF LINEAR OBJECTS UNDER CONSTRAINTS ON THE PHASE COORDINATES

Methods for solving the problem of synthesizing a controlled system under specified constraints on system indicators, that is, methods for the solution of the so-called basic control problem, are presented. Conditions for the solvability of this problem for processes described by a linear system of differential equations under inequality constraints on the linear functions of the phase coordinates and on the controls at discrete time instants are examined. The parametric synthesis problem is reduced to a linear system of inequalities in the system parameters. Theorems which yield the necessary or sufficient conditions for its solvability and, correspondingly, the solvability of the basic control problem, are proven.