About One Approach to Numerical Solution of Nonlinear Optimal Speed Problemsстатья
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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:Optimal speed problems are among the most important problems of the theory ofcontrolled systems. In the qualitative theory of nonlinear speed problems one of the mainresults is the Pontryagin maximum principle. For the numerical solution of nonlinear speedproblems, along with methods based on the maximum principle, methods of reducing toauxiliary problems of optimal control using linearization, parameterization, discretization,and other techniques are widely used. The complexity of numerical methods is determinedby the number of iterations to nd a solution to the speed problem with a given accuracy.A universal computational procedure that is eective for calculating a variety of speedproblems does not currently exist. Therefore, it is actual to develop special approachesto reduce the amount of calculations and reduce the number of iterations. The paperproposes a new approach based on the reduction of a nonlinear speed problem to anauxiliary optimization problem with mixed control functions and parameters. To searchfor a solution to the emerging auxiliary problem, a specially developed form of conditionsfor nonlocal improvement of admissible control in the form of a fixed-point problem ofthe control operator, and a constructed iterative algorithm for successive improvement ofadmissible controls are used. Approbation and comparative analysis of the computationalefficiency of the proposed fixed point approach is carried out on known models of optimalspeed problems.