Duality Principle Use at Solution of Inverse Problems of Test Result Assessment

Abstract

ИСПОЛЬЗОВАНИЕ ПРИНЦИПА ДВОЙСТВЕННОСТИ ПРИ РЕШЕНИИ ОБРАТНЫХ ЗАДАЧ ОЦЕНКИ РЕЗУЛЬТАТОВ ИСПЫТАНИЙС точки зрения возможности использования принципа двойственности рассмотрена типовая об-ратная задача, часто возникающая при оценке со-стояния динамических систем по результатам их испытаний в режимах пассивного эксперимента, в частности при их штатной эксплуатации. Показано, что при решении типовых обратных задач оценки результатов испытаний возможно и целесообразно использование методологии двойственности с анало-гичными задачами теории оптимального управления.Ключевые слова: двойственность, квадра-тичный критерий, обратная задача, динамическая система, автоматическое регулирование. DUALITY PRINCIPLE USE AT SOLUTION OF INVERSE PROBLEMS OF TEST RESULT ASSESSMENTThe purpose of this work was a consideration of one of possible ways to improve methodologies for the solution of standard inverse problems on the basis of dual method attraction in the solution of the other applied problem considered in the theory of optimum management. As a reason for such an approach, according to the authors, is that both problems (identification and management) possess reciprocal duplicity as pursue an end object identical from the mathematical point of view -definition of the extremum of a certain functional. When such a functional is accepted in a quadratic form appears a possibility to pass from numerical approximate methods of solution to analytical ones. From the stand point of the possibility to use this principle in this paper there is considered a standard inverse problem often arising at the assessment of dynamic systems states according to the results of their tests in modes of a passive experiment, in particular, at their normal operation. It is shown that at the solution of standard inverse problems of the assessment of test results it should be possible to use purposefully the methodologies of duality with analogous problems of the theory of optimum management. The approaches considered in the paper passed practical realization at the solution of some inverse problems.