Generalized Implicit Function Theorem and its Application to Parametric Optimal Control Problems

Kostina, Ekaterina and Kostyukova, Olga

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Abstract

Many problems in physics and mathematics may be reduced to solving equations depending on a parameter. The justi cation of the existence of solutions to the equations and the sensitivity analysis maybe conducted based on Implicit Function Theorem (IFT) under certain regularity assumptions. Provided the regularity assumptions do not hold, generalizations of IFT are needed in order to study solutions to the equations. The paper focuses on a particular generalization of IFT which is then applied to a parametric linear time-optimal control problem.

Item Type:	Preprint
Series Name:	IWR-Preprints
Date:	2005
Faculties / Institutes:	Service facilities > Interdisciplinary Center for Scientific Computing
Subjects:	510 Mathematics
Controlled Keywords:	Satz ueber implizite Funktion, Bifurkationen, parametrische zeit-optimale Steuerungsprobleme, Parameterabhängigkeit
Uncontrolled Keywords:	implicit function theorem , bifurcations , parametric time-optimal control problems , dependence on parameter