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Approximate, limiting and generalized trajectories of feedback differential systems

✍ Scribed by Ştefan Mirică

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
152 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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)

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