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Determination of Vertices and Edges in a Parametric Polytope to Analyze Root Indices of Robust Control Quality

International Journal of Automation and computing 2019年第6期16卷 828-837页

作者： Sergey Gayvoronskiy tatiana ezangina Ivan Khozhaev Viktor Kazmin School of Computer Science and Robotics National Research Tomsk Polytechnic University

The research deals with the methodology intended to root robust quality indices in the interval control system, the parameters of which are affinely included in the coefficients of a characteristic polynomial. To determine the root quality indices we propose to depict on the root plane not all edges of the interval parametric polytope(as the edge theorem says), but its particular vertex-edge route. In order to define this route we need to know the angle sequence at which the edge branches depart from any integrated pole on the allocation area. It is revealed that the edge branches can integrate into the route both fully or partially due to intersection with other branches. The conditions which determine the intersection of one-face edge images have been proven. It is shown that the root quality indices can be determined by its ends or by any other internal point depending on a type of edge branch. The conditions which allow determining the edge branch type have been identified. On the basis of these studies we developed the algorithm intended to construct a boundary vertex-edge route on the polytope with the interval parameters of the system. As an illustration of how the algorithm can be implemented, we determined and introduced the root indices reflecting the robust quality of the system used to stabilize the position of an underwater charging station for autonomous unmanned vehicles.

关键词： Robust control parametric uncertainty parametric polytope interval parameters system analysis

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