1. Examining Committee:
Dr. Ya-Jun Pan (Supervisor)
Dr. Jason Gu (External)
Dr. Robert Bauer (Internal)
Moderator: Dr. George Jarjoura
- Presented by Ajinkya Pawar (M.A.Sc Candidate)
Leader-following Consensus
of Multi-agent System with
Communication Constraints
using Lyapunov-based
Control

2. Presentation Outline
 Introduction to Multi-agent Systems (MAS)
 Leader-following Consensus of MAS
 Consensus Control of MAS
 Simulink Results
 Experimental Setup and Results
 Conclusion and Future Works
2

3. Multi-agents Systems (MAS)
 An Agent is defined as a computational entity
that can sense and act as well as decide on its
actions in accordance with some assigned
tasks or goals.
 Multi-agent System (MAS) is a specific type of
system which composes of several agents that
interact with each other to achieve certain
objectives.
Agent
Environment
Sensory
Input
Action
Output
Source: http://www.dcsc.tudelft.nl/Research
3

4. Advantages of Multi-agents Systems (MAS)
 Distributes computational resources and capabilities.
 MAS models problems in terms of autonomous interacting agents.
 MAS efficiently retrieves and filters the global information states.
 Can work and also find solutions in conditions where it is difficult for human
to reach or even to work.
 Comparing with independent working of agents, MAS seems more reliable
and more efficient.
 Decentralized MAS eradicates the system failure chances. 4

5. Applications of Multi-agents Systems (MAS)
Formation Control
 Autonomous Formation Flight (AFF).
 Unmanned Aerial Vehicles (UAVs)
significantly attracted military’s interest
because of low cost, easy maneuver, high
stability and zero casualty.
 AFF control laws utilize a combination of local
and global information states.
https://ocw.mit.edu/courses/aeronautics-
and-astronautics/16-886
 NASA, in 2002,
implemented AFF by
using F/A-18 fighters.
5

6. Applications of Multi-agents Systems (MAS)
Rendezvous and Cooperative Surveillance
 Rendezvous problem involves bringing a
collection of vehicles to a common location at a
common time.
 Cooperative Surveillance involves using several
vehicles to maintain a centralized or
decentralized description of the state of a
geographical area.
http://users.cms.caltech.edu/~murray/p
reprints/mur07
 Information states about
spatially fixed or
moving entities are part
of surveillance. 6

7. Applications of Multi-agents Systems (MAS)
Environmental Sampling
 Autonomous Ocean Sampling Network (AOSN)
consists of robotic vehicles that are used for
“adaptive sampling”.
 The vehicles traverse random paths to record
observations. This approach allows the sensors to
be positioned in areas where they are highly
efficient.
http://users.cms.caltech.edu/~mu
rray/preprints/mur07
 Cooperative control
strategy is used to
control motion of
vehicles. 7

8. Applications of Multi-agents Systems (MAS)
Intelligent Transport System
 Make use of modern communication and
information technology to increase the efficiency
of transport management system in order to
optimize vehicle life, fuel efficiency, safety and
traffic.
 California Partners for Advanced Transit and
Highways (PATH) demonstrated automatic
highway system.
http://www.horiba-mira.com/MIRA/
 Also suitable for air
traffic control.
8

9. Thesis Motivation
9
 Wireless networked communication control systems pose different
challenges to control engineers like time-delays, packet data loss,
switching topologies, noise, quantization error etc.
 Very few literature on the leader-following consensus of MAS with
presence of both time delays as well as packet dropout.
 Lyapunov-based control methodology to be adopted for consensus

10. Leader-follower Consensus of MAS
Leader
Follower 3Follower 1 Follower 2
Source: http://users.ece.gatech.edu/
 Agents are differentiated as leaders and followers.
 Leader agent follows pre-assigned trajectory or
generates it’s own trajectory.
 Follower agent tracks the leader’s trajectory.
 Follower agent tries to reduce its distance from the
leader agent.
 Leader-following consensus can be easily
extended to leader-formation control.
10

11. Multi-agent System Dynamics
11

12. Multi-agent System Dynamics
12

13. Multi-agent System Dynamics with Constant Time-Delay
and Packet Loss
13

14. 14
Multi-agent System Dynamics with Constant Time-Delay
and Packet Loss

15. 15
Multi-agent System Dynamics with Constant Time-Delay
and Packet Loss

16. Multi-agent System Error Dynamics with Constant Time-
Delay and Packet Loss
16

17. Multi-agent System Error Dynamics with Constant Time-
Delay and Packet Loss
17

18. Multi-agent System Error Dynamics with Constant Time-
Delay and Packet Loss
18

19. Multi-agent System and Error Dynamics with Time-
varying Delay and Packet Loss
19

20. Consensus Control of MAS with Constant Time-Delay
and Packet Loss
20

21. Consensus Control of MAS with Constant Time-Delay
and Packet Loss
21

22. Consensus Control of MAS with Constant Time-Delay
and Packet Loss
22

23. Consensus Control of MAS with Constant Time-Delay
and Packet Loss (Final LMI)
23

24. Consensus Control of MAS with Time-varying Delay and
Packet Loss
24

25. Consensus Control of MAS with Time-varying Delay and
Packet Loss
25

26. Simulink Results
26
There are five conditions for which Simulink results are plotted but categorized
in three cases.
 Case 1: Effect of different data loss rate without time delays on consensus of
MAS.
 Case 2: Effect of time delays on consensus of MAS, where one condition is
with constant time-delay and other condition with time-varying delay.
 Case 3: Effect of increasing the number of agents on consensus of MAS,
where one condition is without time-delay and other condition with constant
time delay.

27. Simulink Results (Case 1)
27
Case 1: Effect of different data loss rate without time delays on consensus
of MAS.
 The directed graph topology for this case is,
 The adjacency and Laplacian matrix are:

28. Simulink Results (Case 1)
28
Example 1: Data Loss Rate, r = 0%
i.e. no data loss rate (ideal condition)
Example 2: Data Loss Rate, r = 10%

29. Simulink Results (Case 1)
29
Example 3: Data Loss Rate, r = 20% Example 4: Data Loss Rate, r = 30%

30. Simulink Results (Case 1)
30
Example 5: Data Loss Rate, r = 80% Example 6: Data Loss Rate, r = 98%

31. Simulink Results (Case 1)
31
 Summary of the effect of increase in data loss rate on consensus time
Example
Data Loss Rate in
%
Consensus Time
(seconds)
1 0 19
2 10 27
3 20 36
4 30 102
5 80 300
6 98 1200 or inf

32. Simulink Results (Case 2)
32
Case 2: Effect of time delays on consensus of MAS
 The directed graph topology for this case is,
 The adjacency and Laplacian matrix are:

33. Simulink Results (Case 2 – Condition 1)
33
Condition 1: Effect of constant time delay and fixed data loss rate at 10%
Example 1: Data Loss Rate, r = 10%
and Constant time-delay = 0.001
seconds or 1 millisecond
Example 2: Data Loss Rate, r = 10%
and Constant time-delay = 0.005
seconds or 5 milliseconds

34. Simulink Results (Case 2 – Condition 1)
34
Condition 1: Effect of constant time delay and fixed data loss rate at 10%
Example 3: Data Loss Rate, r = 10%
and Constant time-delay = 0.01
seconds or 10 milliseconds
Example 4: Data Loss Rate, r = 10%
and Constant time-delay = 0.1
seconds or 100 milliseconds

35. Simulink Results (Case 2 – Condition 1)
35
 Summary of the effect of increase in constant time-delay at fixed data
loss rate of 10% on consensus time
Example
Time Delay
(milliseconds)
Consensus Time
(seconds)
1 1 33
2 5 34.5
3 10 37
4 100 41

36. Simulink Results (Case 2 – Condition 2)
36
Condition 2: Effect of time-varying delay and fixed data loss rate at 10%
Example 1: Data Loss Rate, r = 10% and
Time-varying delay= 0.001 seconds to
0.01 second
Example 2: Data Loss Rate, r = 10%
and Constant time-delay = 0.01
seconds to 0.1 second

37. Simulink Results (Case 2 – Condition 2)
37
Condition 2: Effect of time-varying delay and fixed data loss rate at 10%
Example 3: Data Loss Rate, r = 10%
and Time-varying delay= 0.001
seconds to 0.1 second
Example 4: Data Loss Rate, r = 10%
and Constant time-delay = 0.001
second to 0.5 second

38. Simulink Results (Case 2 – Condition 2)
38
 Summary of the effect of increase in range of time-varying delay at
fixed data loss rate of 10% on consensus time.
Example
Time-Varying
Delay Range
(milliseconds)
Consensus Time
(seconds)
1 1-10 34
2 10-100 36
3 1-100 46
4 1-500 103

39. Simulink Results (Case 3)
39
Case 3: Effect of increase in number of agents on consensus of MAS
 The directed graph topology for this case is,
 The adjacency and Laplacian matrix are:

40. Simulink Results (Case 3 – Condition 1)
40
Condition 1: Effect of increase in number of agents with no time delay
and 10 % Data Loss Rate

41. Simulink Results (Case 3 – Condition 2)
41
Condition 2: Effect of increase in number of agents with constant time
delay of 1 millisecond and 10 % Data Loss Rate

42. Simulink Results (Case 3)
42
 Summary of the effect of increase in number of agents with a no time
delay case and a constant time delay case.

43. Experimental Setup
43
Omron-Adept Pioneer P3-DX Mobile Robot
 16 Ultrasonic Sensors (8 Front and 8 Rear)
 Max Speed: 1.6 m/s
 Max Payload: 23 kg
 Motor with 500 tick encoder
 Three hot swappable 9Ah sealed batteries
Source: http://www.cyberbotics.com/

44. Experimental Setup
44
Communication Channels

45. Experimental Setup
45
ARIA- Advanced Robot Interface for Applications

46. Experimental Result
46
Pioneer Robot Modeling
 Converted Single-Integrator system:
 In Discrete Time System:
 Control Gain:
0.5638 0
0 0.8571

47. Experimental Result
47
Experimental Result for 10% Data Loss Rate and 0.5 second Constant Time-
delay for one virtual leader and two follower agents

48. Video Of Experiment performed
48

49. Conclusions
• A novel consensus algorithm for the MAS in the event of communication
link failure over the network was developed and tested.
• The permissible value of data loss rate that can be permissible is 20%
though it can be observed that the consensus is still possible for higher
percentages of data loss rates.
• The consensus time for higher data loss rates are not feasible, for which
there needs to be threshold range of consensus time within which the
consensus if achieved should be treated as feasible.
• For, constant time-delay, the consensus time is permissible till 30 to 40
seconds.
49

50. Conclusions
• Increasing the data loss rate increases the consensus time, but the feasible
result was observed till 10% data loss rate.
• The experimental setup was also carried out at data loss rate of 10%.
• For constant time-delay, the increase in value of time delay increases the
consensus time. For the considered system, the permissible value of time
delay is limited to the sampling time i.e. 0.1 second or 100 milliseconds.
50

51. Future Works
• Can be applied to higher order dynamics.
• Time delays higher than the sampling period should be considered
as condition for controller design.
• Switching topology case can be considered.
51

52. Author Publication List
Conference Paper:
 A. Pawar and Y.J. Pan, "Leader-following Consensus Control of Multi-
Agent Systems with Communication Delays and Random Packet Loss",
In Proceedings of the IEEE American Control Conference, June 2016, Boston,
USA, pp.4464-4469.
Journal Paper:
 X. Gong, Y.J. Pan and A. Pawar, "A Novel Leader Following Consensus
Approach for Multi-Agent Systems with Data Loss", International Journal of
Control, Automation and Systems, Accepted, April 2016.
52