Invariants and first integrals for a special case of a controlled process in an active aviation system

Authors

  • Володимир Олександрович Касьянов National Aviation University Kosmonavta Komarova av., 1, Kyiv, 03680, Ukraine
  • Андрій Вікторович Гончаренко National Aviation University Kosmonavta Komarova av., 1, Kyiv, 03680, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.14672

Keywords:

Hamiltonian, constant, multi-alternativeness, conflict, safety, functional, preference, entropy, variation

Abstract

In this work it has been found Hamiltonians for the theoretically considered, one of the simplest particular cases of a variational problem of control in an active aviation system acting in conditions of multi-alternativeness and conflicts. The presented researches have been performed for a case when the independent variable, that is time, is not present in the functionals explicitly. The entropies of the functionals are different, even if they have the same formal view of notation, because they include different preferences functions which contain different effectiveness functions.

The considered, in these researches, particular cases are derived from the general view functional with the cognitive function of the general form for the studied eleven special cases.

The sought conserved values have been found, and they are the Hamiltonians which is theoretically substantiated and stipulated by the absence of the independent variable in the functionals in the explicit view.

It is fulfilled the mathematical modeling with the Hamiltonian in the special case for the obtained with the help of the Euler-Lagrange equations the canonical distributions of the individual preferences for the given functionals; the differential equations of the second order for finding extremals of the controlling functions of the functionals. Plotted corresponding diagrams

Author Biographies

Володимир Олександрович Касьянов, National Aviation University Kosmonavta Komarova av., 1, Kyiv, 03680

Professor

Department of Mechanics

Андрій Вікторович Гончаренко, National Aviation University Kosmonavta Komarova av., 1, Kyiv, 03680

PhD

Department of Mechanics

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Published

2013-06-20

How to Cite

Касьянов, В. О., & Гончаренко, А. В. (2013). Invariants and first integrals for a special case of a controlled process in an active aviation system. Eastern-European Journal of Enterprise Technologies, 3(3(63), 10–13. https://doi.org/10.15587/1729-4061.2013.14672

Issue

Vol. 3 No. 3(63) (2013): Control systems

Section

Control systems

License

Copyright (c) 2014 Володимир Олександрович Касьянов, Андрій Вікторович Гончаренко

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