NDLI: Asymmetric control achieves size-independent stability margin in 1-D flocks

Content Provider	IEEE Xplore Digital Library
Author	He Hao Barooah, P.
Copyright Year	2011
Description	Author affiliation: Univ. of Florida, USA (He Hao; Barooah, P.)
Abstract	We consider the stability margin of a large 1-D flock of double-integrator agents with distributed control, in which the control at each agent depends on the relative information from its nearest neighbors. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of the flock decays to 0 as $O(1/N^{2}),$ where N is the number of agents. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin can be improved to O(1/N). In this paper, we show that, in fact, with asymmetric control the stability margin of the closed-loop can be bounded away from zero uniformly in N. Asymmetry in control gains thus makes the control architecture highly scalable. We establish the results through distinct routes, using state-space analysis and also using a partial differential equation (PDE) approximation. Numerical verifications are also provided to corroborate our analysis.
Starting Page	3458
Ending Page	3463
File Size	203354
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6160339
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability analysis Eigenvalues and eigenfunctions Numerical stability Laplace equations Mathematical model Symmetric matrices Boundary conditions
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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