Geodesic
Asymptotics of Optimal Synthesis for One Class of Extremal Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 95-124

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The asymptotics of an optimal control while approaching the origin is found for a class of mean square deviation minimization problems with a unilateral force. The asymptotics is described by a series of impulses of maximal amplitude that decrease in time and have the support in the neighborhoods of points of a certain infinite arithmetic progression. The results are applied to the investigation of controlled populational dynamics described by the Lottka–Volterra–Kolmogorov equations. 
@article{TM_2001_233_a3,
     author = {M. I. Zelikin and L. F. Zelikina and R. Hildebrand},
     title = {Asymptotics of {Optimal} {Synthesis} for {One} {Class} of {Extremal} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {95--124},
     publisher = {mathdoc},
     volume = {233},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_233_a3/}
}
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M. I. Zelikin; L. F. Zelikina; R. Hildebrand. Asymptotics of Optimal Synthesis for One Class of Extremal Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations. Certain mathematical problems of optimal control, Tome 233 (2001), pp. 95-124. http://geodesic.mathdoc.fr/item/TM_2001_233_a3/