Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 2

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Free algebras and noncommutative power series in the analysis of nonlinear control systems: an application to approximation problems

100%
Sklyar G., Ignatovich S.
Instytut Matematyczny Polskiej Akademii Nauk
EN
The paper contains a consistent presentation of the approach developed by the authors to analysis of nonlinear control systems, which exploits ideas and techniques of formal power series of independent noncommuting variables and the corresponding free algebras. The main part of the paper was conceived with a view of comparing our results with the results obtained by use of the differential-geometric approach. We consider control-linear systems with m controls. In a free associative algebra with m generators (which can be thought of as a free algebra of iterated integrals), a control system uniquely defines two special objects: the core Lie subalgebra and the graded left ideal. It turns out that each of these two objects completely defines a homogeneous approximation of the system. Our approach allows us to propose an algebraic (coordinate-independent) definition of the homogeneous approximation. This definition provides the uniqueness of the homogeneous approximation (up to a change of coordinates) and gives a way to find it directly, without preliminary finding privileged coordinates. The presented technique yields an effective description of all privileged coordinates and an explicit way of constructing an approximating system. In addition, we discuss the connection between the homogeneous approximation and an approximation in the sense of time optimality.
2
Content available remote

Controlling a non-homogeneous Timoshenko beam with the aid of the torque

94%
Sklyar G., Szkibiel G.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 3
587-598
EN
Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C⁰-continuous semigroups may be applied.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.