Geodesic
Pursuit Problem of Low-Maneuverable Objects with a Ring-Shape Terminal Set
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 25-31

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In this paper, we consider a pursuit problem for two moving objects, a pursuer and an evader. The objects move in the same plane under the influence of controlled forces directed always perpendicular to their velocities. The laws of variation of these forces are determined by first-order controllers. The capture is determined by the condition that the relative distance between the objects belongs to a segment with positive endpoints. For the problem considered, we construct a control of the pursuer that guarantees the catch.
Keywords: pursuit problem, control, terminal set. 
@article{INTO_2018_148_a4,
     author = {I. V. Izmest'ev and V. I. Ukhobotov},
     title = {Pursuit {Problem} of {Low-Maneuverable} {Objects} with a {Ring-Shape} {Terminal} {Set}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {25--31},
     publisher = {mathdoc},
     volume = {148},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_148_a4/}
}
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I. V. Izmest'ev; V. I. Ukhobotov. Pursuit Problem of Low-Maneuverable Objects with a Ring-Shape Terminal Set. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 25-31. http://geodesic.mathdoc.fr/item/INTO_2018_148_a4/