Geodesic
Singularities' of Optimal-Time Function in One Class of Optimal-Time Control Problems Construction Algorithms
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 30-41

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Singular lines and nonsmooth singularities of cost function in one class of optimal-time problems are studied. Equations for their end points are written. Their relation with the geometry of the goal set is shown. Connection of the optimal-time problem and the first order PDE with boundary condition is ascertained. Examples of some problems' solving and graphs of solutions are given.
Keywords: optimal-time control problem, disperse line, pseudoverticle of the set. 
@article{VUU_2010_3_a4,
     author = {A. A. Uspenskii and P. D. Lebedev},
     title = {Singularities' of {Optimal-Time} {Function} in {One} {Class} of {Optimal-Time} {Control} {Problems} {Construction} {Algorithms}},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {30--41},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_3_a4/}
}
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A. A. Uspenskii; P. D. Lebedev. Singularities' of Optimal-Time Function in One Class of Optimal-Time Control Problems Construction Algorithms. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 30-41. http://geodesic.mathdoc.fr/item/VUU_2010_3_a4/