Linear Control Systems on Nilpotent Lie groups
Tez Türü: Yüksek Lisans
Tezin Yürütüldüğü Kurum: Universidad Catolica del Norte, Facultad de Ciencias, Departamento de Matematica, Şili
Tez Danışmanı: Victor Ayala
Tezin Onay Tarihi: 1999
Tezin Dili: İngilizce
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Özet:
In this thesis, we are working in Differential Geometric Control Theory. Two branches of mathematics, differential geometry and the Lie Theory are mainly involved. The thesis is divided into seven chapters. We start in the first chapter recalling some preliminaries on Lie groups and their Lie algebras
and then in the next one giving a brief introduction to control systems as a first motivation.
Our principal interest throughout this thesis is to give a contribution on a new class of control systems, Linear Control Systems on Lie groups introduced in a paper published by the American Mathematical
Society Series : Symposia in Pure and Applied Mathematics, 1998. In this connection, starting from the third chapter we especially deal with this class and give new results.
In particular, the contributions of the work are arranged into the last 4 chapters of the thesis. In fact, in Chapter 4 we establish a result about null controllable set containing some topological properties and extend well-known facts on null controllability property for linear control systems on Rn to linear control systems on Lie groups. We give a global sufficient condition to the null controllability of this class of control systems.
In Chapter 5, we introduce some associated systems to a given linear control system one which is to analize local controllability on a connected Lie group G and, one which is to study that system on a simply connected and nilpotent Lie group case.
In Chapter 6, we turn our interest to another fundamental problem in Control Theory, observability. The work in this section of the thesis is also related to [ ] and indeed we generalize the notion of linear pair as introduced in the paper published by Comput. Appl., Math., 1997. As a matter of fact, we extend all the results appear in [ ] and obtain more general results for general linear pairs where the dynamics of our system is given by a vector field in the normalizer.
We finish the thesis with the Chapter 7. In this part, we construct some original computational algorithms on the direction of our needs which will appear later in details.