Optimal reservation of controlsystems with sliding reseve

A. O. Dovgopola, A. I. Kosolap

Abstract


Abstract.  Purpose. We consider the problem of optimal reservation of control systems with sliding reserve. Such problems arise in  the  design  of  complex  systems.  To  improve  the  reliability  of  operation  of  such  systems  of  its  elements  are  duplicated.  Thi s increases system cost and improves its reliability. A math ematical model    whith sliding reseve  of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of branches and bounds, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension.  Methodology.  In the work for solving redundancy uses a new method for accurate quadratic regularization.  Findings.  This method allows you to convert the original discrete problem to the maximization of mu lti vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straight-dual interior point  methods.  Originality.  Currently,  it  is  the  best  method  for  local  optimization  of  nonlinear  problems.  Transformed  the  task includes  a  new  auxiliary  variable,  which  is  determined  by  dichotomy.  Practical  value.  There  have  been  numerous  comparative numerical experiments in problems  of optimal reservation  of control systems  with sliding reseve. These  experiments  confirm the effectiveness of the method of precise quadratic regularization for solving problems of  optimal reservation of control systems with sliding reseve.


Keywords


backup system; optimization; multiextremal problems; the exact method of quadratic regularization; sliding reseve

References


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Birolini A. Reliability Engineering: Theory and Practice. Springer, 2014, 630 p.

New Computational Methods in Power System Reliability. EditorElmakias D.Berlin,Heidelberg, Springer-Verlag, 2008. 419 p.

Nocedal J.and Wright S. J. Numerical optimization. Springer, 2006, 685 p.


GOST Style Citations


1.  Косолап,  А.  И.  Глобальная  оптимизация.  Метод  точной  квадратичной  регуляризации  /  А.  И.  Косолап  –Днепропетровск: ПГАСА, 2015 – 164 с.

2.  Львович,  Я.Е.  Генетический  алгоритм  решения  многокритериальной  задачи  повышения  надежности резервирования / Я.Е. Львович, И.Л. Каширина, А.А. Тузиков // Информационные технологии. – 2012. – № 6. – С. 56–60.

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6.  Birolini, A. Reliability Engineering: Theory and Practice /A. Birolini.- Springer, 2014.- 630 p.

7.  New  Computational  Methods  in  Power  System  Reliability/Editor  D.  Elmakias.-  Berlin,  Heidelberg:  Springer-Verlag, 2008.- 419 p.

8.  Nocedal, J. Numerical optimization / J. Nocedal, S. J. Wright. – Springer, 2006. – 685 p.



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