Title :
Nonlinear cross Gramians and gradient systems
Author :
Ionescu, Tudor C. ; Scherpen, Jacquelien M A
Author_Institution :
Groningen Univ., Groningen
Abstract :
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Keywords :
gradient methods; linear systems; nonlinear control systems; gradient systems; nonlinear Hankel operator; nonlinear cross Gramians; symmetric linear systems; variational system; Control systems; Controllability; Eigenvalues and eigenfunctions; Linear systems; Mathematics; Nonlinear control systems; Nonlinear equations; Nonlinear systems; Observability; Reduced order systems;
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2007.4434707