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ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337
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On Extremal Step-by-Step Realization of Sliding Modes
RÉSUMÉ
For a controllable differential system uniform approximation of sliding modes was considered by means of trajectories generated by piecewice-constant controls. The conditions of solution uniqueness associated with each control were not imposed. Two discrete rules of extremal shift were investigated. It was shown that 1) by a discrete version of Kryazhimskii method one can approximate some trajectories of the bundle generated by the given generalized control; 2) there exist generalized trajectories which are not approximated by admissible trajectories; 3) if the controllable system satisfies the conditions of Kanke general uniqueness theorem, then any arbitrary sliding mode is approximated by Krasovskiy extremal shift rule.
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