The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ON THE ROBUSTNESS OF CONTINUOUS TRAJECTORIES OF THE NONLINEAR CONTROL SYSTEM DESCRIBED BY AN INTEGRAL EQUATION

  • Nesir Huseyin (Department of Mathematics and Science Education, Sivas Cumhuriyet University) ;
  • Anar Huseyin (Department of Statistics and Computer Sciences, Sivas Cumhuriyet University)
  • Received : 2023.01.23
  • Accepted : 2023.03.04
  • Published : 2023.05.31
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Abstract

In this paper the control system described by Urysohn type integral equation is studied. It is assumed that control functions are integrally constrained. The trajectory of the system is defined as multivariable continuous function which satisfies the system's equation everywhere. It is shown that the set of trajectories is Lipschitz continuous with respect to the parameter which characterizes the bound of the control resource. An upper estimation for the diameter of the set of trajectories is obtained. The robustness of the trajectories with respect to the fast consumption of the remaining control resource is discussed. It is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the control resource.

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References

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