V.N. Panovskiy - Student, Moscow Aviation Institute (National Research University). E-mail: panovskiy.v@yandex.ru A.V. Panteleev - Supervisor, Dr. Sc. (Phys.-Math.), Professor, Head of Department 805, Moscow Aviation Institute (National Research University)

In the given work the interval optimization methods (interval explosion search and interval genetic algorithm), which were created by the author, for the solution of the global constrained optimization problem, are considered. Also these algorithms can be used to solve the problem of determination of optimum program control of nonlinear determined dynamic systems. In the modern mathematics a great attention is given to the solution of problems of global optimization and to the synthesis of optimal control of dynamic systems. These problems arise during designing of planes, helicopters and spacecrafts, when the necessity of optimization of characteristic parameters and of creation of control systems arises. Existing numerical methods use different approaches, but their application is connected with various problems: the big computing loadings, requirements to problem statement, difficulties in reaching convergence. Thus, development of new methods of the optimization, which combine the newest mathematical approaches, is the extremely important. Besides, it is necessary to notice that it is extremely important to use and develop heuristic methods. Despite the lack of its strict substantiation, these methods give an acceptable solution of a problem in the majority of significant cases. Heuristic algorithms do not guarantee finding the solution. However an essential advantage of such algorithms is their low computing complexity. This allows to apply them to the solution of problems of the raised difficulty. In aggregate with key singularities of the interval analysis (handling of ranges instead of isolated points, low insistence to problem statement) development of heuristic interval algorithms is the extremely perspective direction. Interval genetic algorithm bases on the properties of natural evolution: inheritance, mutation, selection and crossing-over. To describe the algorithm it is convenient to use definition from genetic: population - a finite set of individuals, which are represented via chromo-somes, chromosomes - ordered sequences of genes, gene - atomic element of genotype, phenotype - set of values which correspond to the given genotype and etc. The developed algorithm supports two variants of encoding: modified binary and ternary (LR). Interval explosion method combines explosion heuristics and interval analysis. Such a combination allows to create an algorithm, which has advantages from both of approaches. The developed algorithm has small number of parameters and there is no need in complicated tuning. Accurate result can be easily obtained. The proposed algorithms were implemented in a software complex. IDE - Microsoft Visual Studio, programming language - C#. In the given work the algorithm and the software of interval explosion method and interval genetic algorithm for the solution of problems of global constrained optimization and of synthesis of optimal program control of nonlinear determined dynamic systems were created. Also solutions of applied problems (group navigation problem), which demonstrate the effectiveness of the algorithm, are demonstrated.

 

1. Shneydor N.A.Missileguidanceandpursuit. Kinematics, dynamicsandcontrol. Cambridge: WoodheadPublishing. 1998. 259 p.
2. Yanushevsky R.Modernmissileguidance. London. CRCPress. 2008. 226 p.
3. Imado F., Miwa S.Fighterevasivemaneuversagainstproportionalnavigationmissile// JournalofAircraft. 1986. V. 23. P. 825−830.
4. Ratnoo A., Shima T.LineofSightGuidanceforDefendinganAircraft// JournalofGuidance, ControlandDynamics. 2011. V. 34. P. 522−532.
5. Jaulin L.Appliedintervalanalysis. London: Springer-Verlag. 2001. 380 p.
6. Hansen E., Walster G.Globaloptimizationusingintervalanalysis. NewYork: MarcelDekker. 2004. 515 p.
7. Panteleev A.V., Bortakovskijj A.S. Teorija upravlenija v primerakh i zadachakh. M.: Vysshaja shkola. 2003. 583 s.
8. Panovskijj V.N. Intervalnyjj geneticheskijj algoritm globalnojj uslovnojj optimizacii // Uspekhi sovremennojj radioehlektroniki. 2014. № 4. S. 71−75.
9. Panovskijj V.N. Prikladnoe primenenie intervalnogo metoda vzryvov // Trudy MAI. 2014. № 73. URL: http://www.mai.ru/science/trudy/published.php-ID=48451.
10. Shapira I., Ben-Asher J.Z.Near-optimalhorizontaltrajectoriesforautonomousairvehicles// Journalofguidance, controlanddynamics. 1997. V. 20. № 4. P. 735−741.