Abstract
AbstractAlgorithms for constructing an optimal result function are proposed for a planar time-optimal control problem with a circular velocity vectorogram and a nonconvex compact target set with a smooth boundary. The differential dependencies for smooth segments of a singular set are revealed, which allows them to be considered and constructed in the form of arcs of integral curves. Various types of characteristic points of the boundary of the target set—so-called pseudo-vertices—are studied. The necessary conditions for their existence are found and formulas giving the coordinates of the projections of the points of the singular set in their neighborhood are obtained. Examples of time-optimal problems for which numerical construction of the functions of the optimal result and their singular sets are carried out are given. The results are visualized.KeywordsTime-optimal problemsOptimal result functionsSingular setsBisectorWave frontsPseudo-vertexCurvatureGeneralized solution
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