Geodesic
On solving approach problems for control systems
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 276-291

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We study the problem of making a control system in a finite-dimensional Euclidean space approach a compact set at a fixed instant of time. The technique presented in the paper for solving the approach problem is based on constructions involving solvability sets. To construct approximately the solvability set, we apply a backward (in time) procedure that involves storing controls selected during the construction of this set. We also give examples of simulation of approach problems for mechanical systems. 
@article{TRSPY_2015_291_a20,
     author = {V. N. Ushakov and V. I. Ukhobotov and A. V. Ushakov and G. V. Parshikov},
     title = {On solving approach problems for control systems},
     journal = {Informatics and Automation},
     pages = {276--291},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a20/}
}
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V. N. Ushakov; V. I. Ukhobotov; A. V. Ushakov; G. V. Parshikov. On solving approach problems for control systems. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 276-291. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a20/