An application of Lie groups in distributed control networks - Robotics Institute Carnegie Mellon University

An application of Lie groups in distributed control networks

George A. Kantor and P. S. Krishnaprasad
Journal Article, Systems & Control Letters, Vol. 43, No. 1, pp. 43 - 52, May, 2001

Abstract

Here we introduce a class of linear operators called recursive orthogonal transforms (ROTs) that allow a natural implementation on a distributed control network. We derive conditions under which ROTs can be used to represent SO(n) for n >= 4. We propose a paradigm for distributed feedback control based on plant matrix diagonalization. To find an ROT suitable for this task, we derive a gradient flow on the appropriate underlying Lie group. A numerical example is presented.

Notes
This research was supported in part by a grant from the Army Research Office under the ODDR&E MURI97 Program Grant No. DAAG55-97-1-0114 to the Center for Dynamics and Control of Smart Structures (through Harvard University) and also by grants from the National Science Foundation's Engineering Research Centers Program: NSFD CDR 8803012, and by a Learning and Intelligent Systems Initiative Grant CMS9720334.

BibTeX

@article{Kantor-2001-8253,
author = {George A. Kantor and P. S. Krishnaprasad},
title = {An application of Lie groups in distributed control networks},
journal = {Systems & Control Letters},
year = {2001},
month = {May},
volume = {43},
number = {1},
pages = {43 - 52},
keywords = {distributed control, sensor/actuator arrays, signal processing, Lie groups, gradient flow},
}