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Approximate solutions of the determinantal assignment problem and distance problems

Leventides, J., Petroulakis, G. and Karcanias, N. (2013). Approximate solutions of the determinantal assignment problem and distance problems. System, Structure and Control, 5(1), pp. 605-610. doi: 10.3182/20130204-3-FR-2033.00097

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.

Publication Type: Article
Publisher Keywords: Linear systems; Structural properties; Output feedback control
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Engineering
School of Mathematics, Computer Science & Engineering > Engineering > Electrical & Electronic Engineering
URI: http://openaccess.city.ac.uk/id/eprint/7283
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