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Title: Simplification of the generalized state equations (English)
Author: Mullari, Tanel
Author: Kotta, Ülle
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 42
Issue: 5
Year: 2006
Pages: 617-628
Summary lang: English
Category: math
Summary: The paper studies the problem of lowering the orders of input derivatives in nonlinear generalized state equations via generalized coordinate transformation. An alternative, computation-oriented proof is presented for the theorem, originally proved by Delaleau and Respondek, giving necessary and sufficient conditions for existence of such a transformation, in terms of commutativity of certain vector fields. Moreover, the dual conditions in terms of 1-forms have been derived, allowing to calculate the new generalized state coordinates in a simpler way. The result is illustrated with an example, originally given by Delaleau and Respondek (see [2]), but solved in an alternative way. (English)
Keyword: generalized dynamics
Keyword: generalized state transformations
Keyword: input derivatives
Keyword: classical state
Keyword: prolonged vector fields
MSC: 93B11
MSC: 93B17
MSC: 93B29
MSC: 93C10
idZBL: Zbl 1249.93094
idMR: MR2283509
Date available: 2009-09-24T20:19:17Z
Last updated: 2015-03-29
Stable URL:
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