Geodesic
On a local synthesis problem for nonlinear systems with integral constraints
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 171-186

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The paper considers the problem of leading a nonlinear control system to the origin of coordinates at a given integral control resource on a finite time interval. We investigate the question of the construction of local control synthesis that solves the problem, assuming that the time interval during which the system is moved is sufficiently small. We indicate sufficient conditions under which the problem can be solved by the approximate replacement of the nonlinear system by its linearization in the neighborhood of the origin.
Keywords: nonlinear system, controllability set, integral constraints, linearization, local synthesis, small-time, asymptotics.
Mots-clés : Bellman equation 
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     author = {M. I. Gusev and I. O. Osipov},
     title = {On a local synthesis problem for nonlinear systems with integral constraints},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_2_a1/}
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M. I. Gusev; I. O. Osipov. On a local synthesis problem for nonlinear systems with integral constraints. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 171-186. http://geodesic.mathdoc.fr/item/VUU_2022_32_2_a1/