An application of Lie groups in distributed control networks

Citation
Ga. Kantor et Ps. Krishnaprasad, An application of Lie groups in distributed control networks, SYST CONTR, 43(1), 2001, pp. 43-52
Citations number
24
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
SYSTEMS & CONTROL LETTERS
ISSN journal
01676911 → ACNP
Volume
43
Issue
1
Year of publication
2001
Pages
43 - 52
Database
ISI
SICI code
0167-6911(20010515)43:1<43:AAOLGI>2.0.ZU;2-B
Abstract
Here we introduce a class of linear operators called recursive orthogonal t ransforms (ROTs) that allow a natural implementation on a distributed contr ol network. We derive conditions under which ROTs can be used to represent SO(n) for n greater than or equal to4. We propose a paradigm for distribute d feedback control based on plant matrix diagonalization. To find an ROT su itable for this task, we derive a gradient flow on the appropriate underlyi ng Lie group. A numerical example is presented. (C) 2001 Elsevier Science B .V. All rights reserved.