Leventides, J., Petroulakis, G. & Karcanias, N. (2013). Approximate solutions of the determinantal assignment problem and distance problems. System, Structure and Control, 5(1), pp. 605610. doi: 10.3182/201302043FR2033.00097

Text
 Accepted Version
Download (221kB)  Preview 
Abstract
The paper introduces the formulation of an exact algebrogeometric problem, the study of the Determinantal Assignment Problem (DAP) in the set up of design, where approximate solutions of the algebraic problem are sought. Integral part of the solution of the Approximate DAP is the computation of distance of a multivector from the Grassmann variety of a projective space. We examine the special case of the calculation of the minimum distance of a multivector in ∧2(ℝ5) from the Grassmann variety G 2(ℝ5). This problem is closely related to the problem of decomposing the multivector and finding its best decomposable approximation. We establish the existence of the best decomposition in a closed form and link the problem of distance to the decomposition of multivectors. The uniqueness of this decomposition is then examined and several new alternative decompositions are presented that solve our minimization problem based on the structure of the problem.
Item Type:  Article 

Uncontrolled Keywords:  Linear systems; Structural properties; Output feedback control 
Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Engineering 
URI:  http://openaccess.city.ac.uk/id/eprint/7283 
Actions (login required)
View Item 
Downloads
Downloads per month over past year