Algorithmic Methods of Variational Calculus

Abstract

In problems of automatic control system optimization it is required to determine the structure of controller, parameters or the law of reference value variation which would guarantee the required quality of control. Methods of variational calculus are often used to solve problems of optimal control when control objects are simple and have mathematical models. But these methods are not universal, it is difficult to use them when objects are defined by logical operators and it is impossible to use them when mathematical model does not exist. The aim of the present work is as follows: by application of optimization methods to create algorithmic variational calculus methods that would allow solving variational calculus problems in cases when mathematical model (functional) of the object is not set by analytical method and it is impossible to apply classical methods. The technique of algorithmic variational calculus method is set in the article, problems of variational calculus with unfixed trajectory ends are formulated in the form of search optimization problems, methods of finding extremals with corners are indicated and examples of solutions of variational calculus problems are presented. Ill. 6, bibl. 4 (in Lithuanian; summaries in English, Russian and Lithuanian).