Abstract
Let us consider the affine control system
which is the object S of the category AS. In the terminology of category theory (see Sec. 1.2), a quotient object of the object S is a pair consisting of a control system S defined by the relations
and an epimorphism, i.e., a morphism ϕ: M → N of the system S into the system \(\tilde s\), that is a surjective mapping. In what follows, we confine ourselves to quotient objects for which the corresponding morphism ϕ is complete and, additionally, a submersion. Recall that, in the terminology of Sec. 2.2, the completeness of a morphism ϕ implies that if F and G are the associated affine distributions of systems (4.1) and (4.2), respectively, then ϕ *|y F(y) = G(ϕ(y)) ∀ y ∈ M. Since ϕ is a submersion, the mapping ϕ is defined by m functionally independent functions
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Elkin, V.I. (1999). Factorization of Control Systems. In: Reduction of Nonlinear Control Systems. Mathematics and Its Applications, vol 472. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4617-3_4
Download citation
DOI: https://doi.org/10.1007/978-94-011-4617-3_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5951-0
Online ISBN: 978-94-011-4617-3
eBook Packages: Springer Book Archive