Geodesic
About the time-optimal problem for one class of two-dimensional bilinear controlled systems
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 3, pp. 7-20

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In the paper one class of bilinear two-dimensional controlled systems is considered. For these systems the bang-bang property of time-optimal control is studied. The bang-bang property is very interesting for applications, because bang-bang controls are very suitable for realization in practice. In the paper some efficient conditions for bang-bang property of time-optimal controls are received. In the capacity as example, it was considered some controlled analog of the L. Richardson model which is well-known in political science.
Keywords: optimal control, bilinear controlled systems, bang-bang property of control, model of L. Richardson. 
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     author = {Mikhail S. Nikolskii},
     title = {About the time-optimal problem for one class of two-dimensional bilinear controlled systems},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {7--20},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2010_2_3_a1/}
}
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Mikhail S. Nikolskii. About the time-optimal problem for one class of two-dimensional bilinear controlled systems. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 3, pp. 7-20. http://geodesic.mathdoc.fr/item/MGTA_2010_2_3_a1/