A numerical study of the stochastic cucker-smale flocking model

Subramanian Ramakrishnan, Balaji R. Sharma, Manish Kumar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the influence of white noise on achieving consensus in a stochastic version of the well known Cucker-Smale model for flocking in multi-agent swarm systems. Our main results based on extensive numerical simulations suggest that while low intensity white noise has little appreciable effects on convergence to consensus in the system, the presence of high intensity white noise can fundamentally alter the flocking characteristics of the model. In particular, our results indicate that the numerical upper bound on a critical system parameter value that guarantees flocking in the deterministic model is no longer valid in the presence of high intensity white noise. In addition, the results also suggest that, interestingly, the influence of noise is independent of the number of agents in the swarm. Finally, we suggest a novel approach using the classical Fokker-Planck formalism as a direction of further analytical work aimed at validating our numerical results.

Original languageEnglish (US)
Title of host publicationASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
Pages333-338
Number of pages6
DOIs
StatePublished - Dec 1 2012
EventASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012 - Fort Lauderdale, FL, United States
Duration: Oct 17 2012Oct 19 2012

Publication series

NameASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
Volume3

Other

OtherASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
CountryUnited States
CityFort Lauderdale, FL
Period10/17/1210/19/12

Fingerprint

White noise
Computer simulation

Cite this

Ramakrishnan, S., Sharma, B. R., & Kumar, M. (2012). A numerical study of the stochastic cucker-smale flocking model. In ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012 (pp. 333-338). (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012; Vol. 3). https://doi.org/10.1115/DSCC2012-MOVIC2012-8860

A numerical study of the stochastic cucker-smale flocking model. / Ramakrishnan, Subramanian; Sharma, Balaji R.; Kumar, Manish.

ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. 2012. p. 333-338 (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012; Vol. 3).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ramakrishnan, S, Sharma, BR & Kumar, M 2012, A numerical study of the stochastic cucker-smale flocking model. in ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012, vol. 3, pp. 333-338, ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012, Fort Lauderdale, FL, United States, 10/17/12. https://doi.org/10.1115/DSCC2012-MOVIC2012-8860
Ramakrishnan S, Sharma BR, Kumar M. A numerical study of the stochastic cucker-smale flocking model. In ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. 2012. p. 333-338. (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012). https://doi.org/10.1115/DSCC2012-MOVIC2012-8860
Ramakrishnan, Subramanian ; Sharma, Balaji R. ; Kumar, Manish. / A numerical study of the stochastic cucker-smale flocking model. ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. 2012. pp. 333-338 (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012).
@inproceedings{900f7d0a024145ecbeeb209147eda5ce,
title = "A numerical study of the stochastic cucker-smale flocking model",
abstract = "We consider the influence of white noise on achieving consensus in a stochastic version of the well known Cucker-Smale model for flocking in multi-agent swarm systems. Our main results based on extensive numerical simulations suggest that while low intensity white noise has little appreciable effects on convergence to consensus in the system, the presence of high intensity white noise can fundamentally alter the flocking characteristics of the model. In particular, our results indicate that the numerical upper bound on a critical system parameter value that guarantees flocking in the deterministic model is no longer valid in the presence of high intensity white noise. In addition, the results also suggest that, interestingly, the influence of noise is independent of the number of agents in the swarm. Finally, we suggest a novel approach using the classical Fokker-Planck formalism as a direction of further analytical work aimed at validating our numerical results.",
author = "Subramanian Ramakrishnan and Sharma, {Balaji R.} and Manish Kumar",
year = "2012",
month = "12",
day = "1",
doi = "10.1115/DSCC2012-MOVIC2012-8860",
language = "English (US)",
isbn = "9780791845318",
series = "ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012",
pages = "333--338",
booktitle = "ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012",

}

TY - GEN

T1 - A numerical study of the stochastic cucker-smale flocking model

AU - Ramakrishnan, Subramanian

AU - Sharma, Balaji R.

AU - Kumar, Manish

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We consider the influence of white noise on achieving consensus in a stochastic version of the well known Cucker-Smale model for flocking in multi-agent swarm systems. Our main results based on extensive numerical simulations suggest that while low intensity white noise has little appreciable effects on convergence to consensus in the system, the presence of high intensity white noise can fundamentally alter the flocking characteristics of the model. In particular, our results indicate that the numerical upper bound on a critical system parameter value that guarantees flocking in the deterministic model is no longer valid in the presence of high intensity white noise. In addition, the results also suggest that, interestingly, the influence of noise is independent of the number of agents in the swarm. Finally, we suggest a novel approach using the classical Fokker-Planck formalism as a direction of further analytical work aimed at validating our numerical results.

AB - We consider the influence of white noise on achieving consensus in a stochastic version of the well known Cucker-Smale model for flocking in multi-agent swarm systems. Our main results based on extensive numerical simulations suggest that while low intensity white noise has little appreciable effects on convergence to consensus in the system, the presence of high intensity white noise can fundamentally alter the flocking characteristics of the model. In particular, our results indicate that the numerical upper bound on a critical system parameter value that guarantees flocking in the deterministic model is no longer valid in the presence of high intensity white noise. In addition, the results also suggest that, interestingly, the influence of noise is independent of the number of agents in the swarm. Finally, we suggest a novel approach using the classical Fokker-Planck formalism as a direction of further analytical work aimed at validating our numerical results.

UR - http://www.scopus.com/inward/record.url?scp=84885896448&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885896448&partnerID=8YFLogxK

U2 - 10.1115/DSCC2012-MOVIC2012-8860

DO - 10.1115/DSCC2012-MOVIC2012-8860

M3 - Conference contribution

AN - SCOPUS:84885896448

SN - 9780791845318

T3 - ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012

SP - 333

EP - 338

BT - ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012

ER -