Figure 3.24: Consensus protocols for sensor networks - Revision history

Murray at 16:35, 28 May 2023

2023-05-28T16:35:52Z

Murray at 16:24, 30 August 2021

2021-08-30T16:24:52Z

Murray at 16:23, 30 August 2021

2021-08-30T16:23:47Z

Murray: Created page with "{{Figure |Chapter=System Modeling |Figure number=24 |Figure title=Consensus protocols for sensor networks |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure..."

2021-08-30T16:22:51Z

Created page with "{{Figure |Chapter=System Modeling |Figure number=24 |Figure title=Consensus protocols for sensor networks |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure..."

New page

{{Figure
|Chapter=System Modeling
|Figure number=24
|Figure title=Consensus protocols for sensor networks
|GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-3.24-consensus.py
}}
[[Image:figure-3.24-consensus_dynamics.png|640px]]

Figure 3.24: Consensus protocols for sensor networks. (b) A simulation demonstrating the convergence of the consensus protocol (3.35) to the average value of the initial conditions.

<nowiki>
# example-3.17-consensus.py - consensus protocols
# RMM, 30 Aug 2021

# Figure 3.24: Consensus protocols for sensor networks. (a) A simple sensor
# net- work with five nodes. In this network, node 1 communicates with node
# 2 and node 2 communicates with nodes 1, 3, 4, 5, etc. (b) A simulation
# demonstrating the convergence of the consensus protocol (3.35) to the
# average value of the initial conditions.

import control as ct
import numpy as np
import matplotlib.pyplot as plt

#
# System dynamcis
#

# Construct the Laplacian corresponding to our network
L = np.array([
[ 1, -1, 0, 0, 0],
[-1, 4, -1, -1, -1],
[ 0, -1, 2, -1, 0],
[ 0, -1, -1, 2, 0],
[ 0, -1, 0, 0, 1]
])

# Now generate the discrete time dynamics matrix
gamma = 0.1
A = np.eye(5) - gamma * L

# Initial set of measurements for the system
x0 = [10, 15, 25, 35, 40]

# Create a discrete time system
sys = ct.ss(A, np.zeros(5), np.zeros(5), 0, dt=True)

# Set up the plotting grid to match the layout in the book
fig = plt.figure(constrained_layout=True)
gs = fig.add_gridspec(3, 2)

#
# (b) A simulation demonstrating the convergence of the consensus protocol
# (3.35) to the average value of the initial conditions.
#

fig.add_subplot(gs[0, 1]) # first row, first column

# Simulate the system
response = ct.initial_response(sys, 40, x0)

# Plot th3 results
for i in range(response.nstates):
plt.plot(response.time, response.states[i], 'b-')

# Label the figure
plt.xlabel("Iteration")
plt.ylabel("Agent states $x_i$")
plt.title("Consensus convergence")

# Save the figure
plt.savefig("figure-3.24-consensus_dynamics.png", bbox_inches='tight')
</nowiki>

@@ Line 1: / Line 1: @@
 {{Figure
 |Chapter=System Modeling
-|Figure number=24
+|Figure number=3.24
 |Figure title=Consensus protocols for sensor networks
 |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/example-3.17-consensus.py

@@ Line 5: / Line 5: @@
 |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-3.24-consensus.py
 }}
-[[Image:figure-3.24-consensus_dynamics.png|640px]]
+[[Image:figure-3.24-consensus_dynamics.png|320px]]
 Figure 3.24: Consensus protocols for sensor networks. (b) A simulation demonstrating the convergence of the consensus protocol (3.35) to the average value of the initial conditions.