Bamieh, B., Jovanovic, M., Mitra, P. P., Patterson, S. (2008) Effect of topological dimension on rigidity of vehicle formations: Fundamental limitations of local feedback. IEEE Conference on Decision and Control. pp. 369-374.
Abstract
We consider the role of topological dimension in problems of network consensus and vehicular formations where only local feedback is available. In particular, we consider the simple network topologies of regular lattices in 1, 2 and higher dimensions. Performance measures for consensus and formation problems are proposed that measure the deviation from average and rigidity or tightness of formations respectively. A common phenomenon appears where in dimensions 1 and 2, consensus is impossible in the presence of any amount of additive stochastic perturbations, and in the limit of large formations. In dimensions 3 and higher, consensus is indeed possible. We show that microscopic error measures that involve only neighboring sites do not suffer from this effect. This phenomenon reflects the fact that in dimensions 1 and 2, local stabilizing feedbacks can not suppress long spatial wavelength "meandering" motions. These effects are significantly more pronounced in vehicular problems than in consensus, and yet they are unrelated to string stability issues. © 2008 IEEE.
| Item Type: | Paper |
|---|---|
| Additional Information: | Meeting Abstract |
| Subjects: | physics > biophysics Publication Type > Meeting Abstract physics |
| CSHL Authors: | |
| Communities: | CSHL labs > Mitra lab |
| Depositing User: | CSHL Librarian |
| Date: | 2008 |
| Date Deposited: | 10 Apr 2012 14:51 |
| Last Modified: | 13 Mar 2018 20:17 |
| URI: | https://repository.cshl.edu/id/eprint/25818 |
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