Method for finding a solution to a linear nonstationary interval ОDЕ system

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Abstract

The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Some numerical examples illustrate the constructed algorithm realization.

Original languageEnglish
Pages (from-to)148-165
Number of pages18
JournalVestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya
Volume17
Issue number2
DOIs
StatePublished - 2021

Scopus subject areas

  • Computer Science(all)
  • Control and Optimization
  • Applied Mathematics

Keywords

  • Differential inclusion
  • Linear nonstationary interval system of ordinary differential equations
  • Support function
  • The steepest descent method

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