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Approximate, limiting and generalized trajectories of feedback differential systems
Author(s) -
Mirică Ştefan
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310252
Subject(s) - differential inclusion , mathematics , counterexample , limiting , conjecture , euler's formula , parameterized complexity , invariant (physics) , tangent , differential (mechanical device) , pure mathematics , mathematical analysis , discrete mathematics , combinatorics , mathematical physics , geometry , mechanical engineering , engineering , aerospace engineering
In view of possible applications in Optimal Control, Differential Games and other fields, we obtain certain invariant characterizations of the limiting Euler trajectories and of the limiting Krassovskii‐Subbotin trajectories of large classes of feedback differential systems defined as parameterized differential inclusions. We prove that these limiting trajectories are Carathéodory solutions of certain associated u.s.c.‐convexified differential inclusions which contain their generalized tangent and contingent directions. In particular, we give a counterexample to a conjecture of Krassovskii and Subbotin (1974) and provide a proof of its correct variant. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)