Strong accessibility and integral manifolds of the continuous-time nonlinear control systems

Autor:	Małgorzata Wyrwas
Rok vydání:	2019
Předmět:	Pure mathematics Integrable system Applied Mathematics Ordinary differential equation Lie algebra Vector field Algebraic number Invariant (mathematics) Nonlinear control Analysis Mathematics Analytic function
Zdroj:	Journal of Mathematical Analysis and Applications. 469:935-959
ISSN:	0022-247X
DOI:	10.1016/j.jmaa.2018.09.045
Popis:	The paper develops the algebraic formalism that is based on the language of ideals and modules associated with the analytic control system given by the ordinary differential equations. Using the Nagano theorem we show how the integral manifolds of Lie algebra of the considered system can be determined by the generators of some ideal of the ring of germs of analytic functions that is invariant with respect to germs of vector fields from the Lie algebra associated with the system. Additionally, basing on the language of ideals and modules the strong accessibility problem is studied. The singular points where the rank of (co)distributions associated to the system is different than at points from their neighbourhoods are considered. Using the germs of one-forms associated with the generators of the ideal one can define the integrable codistribution that in general is not analytic.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2d8ebbcf90078f8edda443c9c08341b8 https://doi.org/10.1016/j.jmaa.2018.09.045 Zobrazit plný text záznamu Full Text from ScienceDirect