Geodesic
On external estimates for reachable sets of nonlinear control systems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 60-69

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The paper is devoted to the problem of constructing external estimates for reachable sets of a nonlinear control system. The estimates are constructed in the form of level sets of smooth functions in the space of states satisfying differential inequalities. In the system under consideration, the linear part is found, for which the corresponding functions are assumed to be known. The method proposed for estimating trajectories of a nonlinear system is based on modifying estimates for the linear part and on applying the comparison principle.
Keywords: control system, reachable set, comparison principle. 
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     author = {M. I. Gusev},
     title = {On external estimates for reachable sets of nonlinear control systems},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a5/}
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M. I. Gusev. On external estimates for reachable sets of nonlinear control systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 60-69. http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a5/