Geodesic
On Estimating the Degree of Nonconvexity of Reachable Sets of Control Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 261-270

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We study the properties of reachable sets of control systems that are linear in control. For the reachable sets of a certain class of such systems, we estimate the growth of their degree of nonconvexity $\alpha $ over time. As an auxiliary result, we establish a relationship between $\alpha $-sets and weakly convex sets in the sense of Vial.
Keywords: Generalized convex set, weakly convex set, reachable set, control system.
Mots-clés : $\alpha $-set 
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     author = {V. N. Ushakov and A. A. Ershov and A. R. Matviychuk},
     title = {On {Estimating} the {Degree} of {Nonconvexity} of {Reachable} {Sets} of {Control} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {261--270},
     publisher = {mathdoc},
     volume = {315},
     year = {2021},
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V. N. Ushakov; A. A. Ershov; A. R. Matviychuk. On Estimating the Degree of Nonconvexity of Reachable Sets of Control Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 261-270. http://geodesic.mathdoc.fr/item/TM_2021_315_a18/