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On Exponential Flocking to the Virtual Leader in Network of Agents With Double-Integrator Dynamics

[+] Author and Article Information
Mohammad Haeri

Advanced Control Systems Lab,
Electrical Engineering Department,
Sharif University of Technology,
Tehran, 11155-4363, Iran

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received August 19, 2011; final manuscript received November 16, 2012; published online March 28, 2013. Assoc. Editor: Rama K. Yedavalli.

J. Dyn. Sys., Meas., Control 135(3), 034504 (Mar 28, 2013) (8 pages) Paper No: DS-11-1261; doi: 10.1115/1.4023242 History: Received August 19, 2011; Revised November 16, 2012

This paper considers flocking to the virtual leader in network of agents with double-integrator. A locally linear algorithm is employed which guarantees exponential flocking to the virtual leader. A lower bound for flocking rate is calculated which is independent of the initial conditions. Simulations are provided to validate the result and it is shown that the calculated rate is not over bound the actual convergence rate. The effect of coefficients of algorithm is investigated and it is shown that the similar results can be inferred from the calculated formula for the convergence rate.

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Figures

Grahic Jump Location
Fig. 3

h1=1, h2=5, c1=1, c2=1, and N=40, actual decadence rate in simulation = 0.4109, calculated rate by Eq. (36) = 0.0092

Grahic Jump Location
Fig. 4

h1=1, h2=5, c1=1, c2=5, and N=150, actual decadence rate in simulation = 0.412, calculated rate by Eq. (36) = 0.0025

Grahic Jump Location
Fig. 1

h1=1, h2=1, c1=1, c2=1, and N=5, actual decadence rate in simulation = 0.9752, calculated rate by Eq. (36) = 0.126

Grahic Jump Location
Fig. 2

h1=1, h2=1, c1=1, c2=5, and N=10, actual decadence rate in simulation = 0.9584, calculated rate by Eq. (36) = 0.0688

Grahic Jump Location
Fig. 5

N=5, actual decadence rate in simulation = 0.126, calculated rate by Eq. (36) = 0.1792

Grahic Jump Location
Fig. 6

N=10, actual decadence rate in simulation = 086, calculated rate by Eq. (36) = 0.0688

Grahic Jump Location
Fig. 7

N=40, actual decadence rate in simulation = 0.0094, calculated rate by Eq. (36) = 0.0092

Grahic Jump Location
Fig. 8

N=150, actual decadence rate in simulation = 0.0025, calculated rate by Eq. (36) = 0.0025

Grahic Jump Location
Fig. 9

Effect of h1, h2=5, c1=1, and c2=5

Grahic Jump Location
Fig. 10

Effect of h2, h1=1, c1=1, and c2=5

Grahic Jump Location
Fig. 11

Effect of c1, h1=1, h2=5, and c2=5

Grahic Jump Location
Fig. 12

Effect of c2, h1=1, h2=5, and c1=1

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