We consider a nonlinear control system in Euclidean space on a finite time interval with controls subject to geometric constraints. The question of constructing lower and upper (by inclusion) approximations of reachable sets of this system is studied. Under certain conditions, estimates are obtained for the discrepancy (in the Hausdorff metric) between the lower and upper approximations of the reachable sets.
Keywords: control system, control, differential inclusion, geometric constraints, reachable set, approximation
Received January 14, 2020
Revised February 6, 2020
Accepted February 10, 2020
Funding Agency: This work was supported by the Russian Foundation for Basic Research (projects no. 18-01-00264 and no. 18-01-00221).
Vladimir Nikolaevich Ushakov, Dr. Phys.-Math. Sci., RAS Corresponding Member, Prof., Krasovskii Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: ushak@imm.uran.ru
Maksim Vadimovich Pershakov, Krasovskii Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: ushak@imm.uran.ru
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Cite this article as: V.N. Ushakov, M.V. Pershakov. On two-sided approximations of reachable sets of control systems with geometric constraints on the controls, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2020, vol. 26, no. 1, pp. 239–255; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2021, Vol. 313, Suppl. 1, pp. S211–S227.
