# IPACS Electronic library

## GEOMETRIC METHOD FOR A PROBLEM OF SYNTHESIS OF THE ROBUST CONTROL ON LINEAR POLYHEDRONS

One of the actual problems of the objectives of control is the problem of synthesizing the law of control, effective under the conditions of various indeterminacy and limitations on motion properties. At the same time the deriving of the robust laws of control is very important under the conditions of illegible data. In this work it is shown, that the solving of the mentioned problem comes to solution of some certain logarithmic correlations from the specially created connected phase plane. As far as smooth phase limitations are concerned, these correlations can be converted into algebraic equations, according to the synthesized law of control. The investigation in the cases of uneven limitations, which describe linear polyhedrons in state space, is performed in this work. It is shown, that in case of being symmetrical to set point of the coordinate system the solvability of synthesizing problem is all defined by the random apex of the polyhedron. If the required condition of the symmetry is not fulfilled, than the minimum amount of the random polyhedron apexes is concerned for analyzing the solvability of the objective. The description (symmetrization) of the phase plane is concerned with the help of the polyhedrons, symmetrical in any way. At the same time the system` indeterminacy is considered straight according to the algebraic correlations of the symmetric polyhedrons` apexes.
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Copyright © 2003—2015 The Laboratory "Control of Complex Systems", IPME RAS
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