THE STABILITY OF SOLUTION OF SYSTEMS WITH UNDEFINED PARAMETERS OPTIMAL DESIGN PROBLEM

Authors

  • V. I. Levin Penza State Technological University, Russia, Russian Federation

DOI:

https://doi.org/10.15588/1607-3274-2013-2-11

Keywords:

system optimization, uncertainty, stability of optimum, variation of parameters, interval mathematics.

Abstract

Our article considers the problem of optimization of incompletely specified functions, namely, functions which parameters are given within range of possible values. It is shown that solution of this problem also requires solving problem of determining stability of optimum of such functions to variation of values of their parameters. A method for obtaining such optimum of incompletely defined functions is presented. Method uses determination of problem. It allows to split original non-deterministic problem into two optimization problem of deterministic functions, which are solved separately. After that solutions are combined into one which is a solution of original problem. The article also provides a method for determining the stability of the optimum found of incompletely defined functions by methods of interval mathematics. We formulate 5 theorems determining the conditions for existence of optimum of incompletely defined function and its resistance to changing the function parameters. Algorithms for verifying the stability function are given

References

Pervozvanskiy A. A. Matematicheskie modeli v upravlenii proizvodstvom, Moscow, Nauka, 1975, 616 p.

Levin V. I. Intervaljnoe diskretnoe programmirovanie, Kibernetika i sistemniy analiz, 1994, No. 6, pp. 91–103.

Libura M. Integer Programming Problems with Inexact Objective Function, Control and Cybernetic, 1980, Vol. 9, No. 4, pp. 189–202.

Timokhin S. G., Shapkin A. V. O zadachah linejnogo programmirovaniya v usloviyah netochnyh dannyh, Ekonomika i matematicheskie metody, 1981, Vol. 17, No. 5, pp. 955–963.

Rothin V. A., Semenova N. V., Sergienko I. V. Voprosy resheniya i issledovaniya odnogo klassa zadach netochnogo celochislennogo programmirovaniya, Kibernetika, 1989, No. 2, pp. 42–46.

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Published

2013-08-13

How to Cite

Levin, V. I. (2013). THE STABILITY OF SOLUTION OF SYSTEMS WITH UNDEFINED PARAMETERS OPTIMAL DESIGN PROBLEM. Radio Electronics, Computer Science, Control, (2). https://doi.org/10.15588/1607-3274-2013-2-11

Issue

No. 2 (2013): Radio Electronics, Computer Science, Control

Section

Mathematical and computer modelling

License

Copyright (c) 2014 V. I. Levin

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