Об одном методе поиска экстремальных управлений в системах с ограничениямистатья
Статья опубликована в журнале из списка RSCI Web of Science
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Scopus
Статья опубликована в журнале из перечня ВАК
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 1 февраля 2021 г.
Аннотация:In the class of controlled systems with constraints, the conditions for improvingand optimality of control are constructed and analyzed in the form of fixed pointproblems. This form allows one to obtain enhanced necessary optimality conditionsin comparison with the known conditions and makes it possible to apply and modifythe theory and methods of fixed points to search for extreme controls in optimizationproblems of the class under consideration. Fixed-point problems are constructed usingthe transition to auxiliary optimal control problems without restrictions with Lagrangefunctionals. An iterative algorithm is proposed for constructing a relaxation sequence ofadmissible controls based on the solution of constructed fixed point problems. The consideredalgorithm is characterized by the properties of nonlocal improvement of admissiblecontrol and the fundamental possibility of rigorous improvement of non-optimal controlssatisfying the known necessary optimality conditions, in contrast to gradient and otherlocal methods. The conditions of convergence of the control sequence for the residual offulfilling the necessary optimality conditions are substantiated. A comparative analysisof the computational and qualitative efficiency of the proposed iterative algorithm forfinding extreme controls in a model problem with phase constraints is carried out.