Sergey Gayvoronskiy, Tatiana Ezangina, Ivan Khozhaev and Viktor Kazmin. Determination of Vertices and Edges in a Parametric Polytope to Analyze Root Indices of Robust Control Quality. International Journal of Automation and Computing, vol. 16, no. 6, pp. 828-837, 2019. https://doi.org/10.1007/s11633-019-1182-y
Citation: Sergey Gayvoronskiy, Tatiana Ezangina, Ivan Khozhaev and Viktor Kazmin. Determination of Vertices and Edges in a Parametric Polytope to Analyze Root Indices of Robust Control Quality. International Journal of Automation and Computing, vol. 16, no. 6, pp. 828-837, 2019. https://doi.org/10.1007/s11633-019-1182-y

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

doi: 10.1007/s11633-019-1182-y
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  • Author Bio:

    Sergey Gayvoronskiy received the Ph. D. degree in control systems engineering from the Tomsk Polytechnic University, Russia in 1990. He is presently an associated professor of the Division for Automation and Robotics at the School of Computer Science and Robotics, National Research Tomsk Polytechnic University, Russia. He was repeatedly awarded by Ministry of Education and Science of Russian Federation, Russian Union of Young Scientists and Tomsk Polytechnic University for his educational and scientific achievements. His research and teaching interests include analysis and synthesis of robust and adaptive control systems for control objects and processes with uncertain parameters. E-mail: saga@tpu.ru ORCID iD: 0000-0002-7156-2807

    Tatiana Ezangina received the Ph. D. degree in system analysis, control and data processing from Tomsk Polytechnic University, Russia in 2016. She is presently a junior researcher of Telecommunications, Electronics and Underwater Geology Laboratory, National Research Tomsk Polytechnic University, Russia. She was repeatedly awarded by the Government of Russian Federation, Ministry of Education and Science of Russian Federation, Tomsk Polytechnic University and other institutions for her scientific achievements. Her research interests include robust and adaptive control system analysis and synthesis, tethered underwater vehicles development and software development. E-mail: eza-tanya@yandex.ru ORCID iD: 0000-0002-4948-5972

    Ivan Khozhaev received the B. Sc. and M. Sc. degrees (honors) in control systems engineering from the Tomsk Polytechnic University, Russia in 2014 and 2016, accordingly. He is presently a Ph. D. student at the Division for Automation and Robotics, the School of Computer Science and Robotics, National Research Tomsk Polytechnic University, Russia. His research interests include robust and adaptive control systems synthesis and analysis, unmanned underwater vehicles development and computational fluid dynamics. E-mail: khozhaev.i@gmail.ru (Corresponding author) ORCID iD: 0000-0002-8874-0200

    Viktor Kazmin received the Ph. D. degree in control systems engineering from the Tomsk Polytechnic University, Russia in 1996. He is presently an associated professor of the Division for Automation and Robotics at the School of Computer Science and Robotics, National Research Tomsk Polytechnic University, Russia. He was repeatedly awarded by Tomsk Polytechnic University for his educational achievements. His research and teaching interests include analysis and synthesis of feedback control systems for internal combustion engines, fundamentals of control theory and automated control.E-mail: kvp@tpu.ru

  • Received Date: 2018-11-11
  • Accepted Date: 2019-04-16
  • Publish Online: 2019-07-16
  • Publish Date: 2019-12-01
  • 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.

     

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