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Matrix Resolving Function in the Nonstationary Linear Group Pursuit Problem Concepting Multiple Capture

Author

Listed:
  • N. N. Petrov

    (Laboratory of Mathematical Control Theory, Udmurt State University, Universitetskaya ul. 1, Izhevsk 426034, Russia)

Abstract

In finite-dimensional Euclidean space, an analysis is made of the problem of pursuit of a single evader by a group of pursuers, which is described by a system of the form żi = Ai(t)zi + ui − v,ui ∈ Ui,v ∈ V. The goal of the group of pursuers is the capture of the evader by no less than m different pursuers (the instants of capture may or may not coincide). Matrix resolving functions, which are a generalization of scalar resolving functions, are used as a mathematical basis of this study. Sufficient conditions are obtained for multiple capture of a single evader in the class of quasi-strategies. Examples illustrating the results obtained are given.

Suggested Citation

  • N. N. Petrov, 2021. "Matrix Resolving Function in the Nonstationary Linear Group Pursuit Problem Concepting Multiple Capture," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 1-13, December.
  • Handle: RePEc:wsi:igtrxx:v:23:y:2021:i:04:n:s021919892150016x
    DOI: 10.1142/S021919892150016X
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