An application of Lie groups in distributed control networks

George A. Kantor and P.S. Krishnaprasad
Systems and Control Letters, Vol. 43, June, 2001, pp. 43-52.


Download
  • Adobe portable document format (pdf) (292KB)
Copyright notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

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.

Keywords
distributed control, sensor/actuator arrays, signal processing, Lie groups, gradient flow

Notes
Number of pages: 10

Text Reference
George A. Kantor and P.S. Krishnaprasad, "An application of Lie groups in distributed control networks," Systems and Control Letters, Vol. 43, June, 2001, pp. 43-52.

BibTeX Reference
@article{Kantor_2001_3866,
   author = "George A Kantor and P.S. Krishnaprasad",
   title = "An application of Lie groups in distributed control networks",
   journal = "Systems and Control Letters",
   pages = "43-52",
   publisher = "Elsevier Science B.V.",
   address = "Holland",
   month = "June",
   year = "2001",
   volume = "43",
}