Application of two-nilpotent lie algebra in control theory

Abstract

This dissertation. is divided into four parts. In the first part, we introduce some notions concerning nilpotent Lie algebras and bilinear control systems. In the second part, we construct an explicit operator B that for a given operator A (written in Jordan normal form) the set {A, B} generates a two-nilpotent Lie algebra i.e. [A,B]=C≠0 and [A,C]=[B,C]=0, and apply this to an optimal control problem. In the third part, we extend the study to a compact operator in a complex Banach space. The fourth part concludes with examples and an application of the optimal error control associated with an observer.