Singular control systems on Lie groups

• Grant number: 99/04687-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 1999
• End date: October 31, 2000
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Luiz Antonio Barrera San Martin
• Grantee: Ayse Kara Hacibekiroglu
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project is concerned with the qualitative study of a new class of control systems that we call ''Singular Control Systems on Lie Groups". The classical linear systems on IRn have been studied since more than four decades. They are very important from theoretical and practical points of view. However, several applications, coming from practical problems, show that many times it is not possible to know• completely the dynamic of the system that models the problem under study. In order to attempt a solution to this difficulty were introduced, in the 1980- decade, the so - called singular systems, (7], (16].The state space for linear and singular systems is IRn. In this project we are looking for to understand a new class of systems on finite dimensional Lie groups. The reasons for this intention are essentially three. First of all, this new class generalizes the following important classes: linear control systems on IRn, singular control systems on IRn, linear control systems on Lie groups including the class of invariant control systems. In particular, it will be important and hard to obtain information about the class that we think to analize… (AU)