estimation and control over networks using event-based transmission methods

공학박사 학위논문
이벤트 기반 전송 방법을 이용한
추정 및 제어
Estimation and Control over Networks using
event-based transmission methods


울 산 대 학 교 대 학 원
전기전자정보시스템공학부
Nguyen Vinh Hao
이벤트 기반 전송 방법을 이용한
추정 및 제어
Estimation and Control over Networks using
event-based transmission methods
지도교수 서 영 수
이 논문을 공학박사 학위 논문으로 제출함
2008 년 12 월


울 산 대 학 교 대 학 원
전기전자정보시스템공학부
Nguyen Vinh Hao
Nguyen Vinh Hao 의 공학박사 학위 논문을 인준함


심 사위원 이홍희 (인)
심 사위원 공형윤 (인)
심 사위원 구인수 (인)
심 사위원 김성원 (인)
심 사위원 서영수 (인)
울 산 대 학 교 대 학 원

2008 년 12 월


Estimation and Control over Networks using
event-based transmission methods



by
Vinh Hao Nguyen



A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Electrical Engineering)
in The University of Ulsan
December, 2008

Acknowledgements


I would like to express my sincere appreciation to my thesis advisor, Prof. Young-
Soo Suh, who has guided me through my Ph.D. research with his patience, vision, and
wisdom. Prof. Suh is never satisfied by mediocre research, he has always encouraged me
to challenge myself with perfectionism and persistence. I thank him for helping me
understand the essence of scientific research and find the real potential of myself. He has
been a continual source of fresh ideas in the process of earning my degree.
I would also like to thank Prof. Hong-Hee Lee and committee members, for taking
their time to review my thesis and be on my committee.
Many thanks to my friends and roommates, who have dealt with my late nights of
thesis work and occasional fits of frustration with good nature. A big thank to my
labmates, for their friendship and their help during my three years in Korea.
Last but not least, I would like to thank my wife, Mrs. Do Thi Kim Chung, for
being such a good friend and providing me supports on every aspect of my life. I would
like to thank my parents for their unconditional and endless love, support, encouragement,
and for taking care of my son during my Ph.D. study.

ii
Abstract


The thesis is concerned with the state estimation and control problem over the
network in which an event-based sampling scheme at sensor nodes is proposed. If the
network speed is high and the traffic is sparse, the traditional periodic sampling approach
has many merits. But when the network bandwidth is limited due to executing tasks of
several nodes, time delay becomes large and randomly varying. Therefore, to avoid these
problems the sensor data transmission rate should be reduced.
In the event-driven sampling scheme, sensor data are transmitted to the estimator
node only if the difference between the current sensor value and the last transmitted one is
greater than a given threshold. The research has shown that the event-based sampling
scheme is more efficient than the periodic sampling one in some situations, especially in
network bandwidth improvement.
The main contribution of thesis is to find the optimal threshold value at each sensor
node which is a trade-off parameter between the sensor data transmission rate and the
control performance. Then the modified Kalman filters are formulated to estimate states of
the system under conditions of system noises, packet loss, etc. At last, the optimal LQG
controllers are set up to solve the control problem over the network.
The simulation and experimental results have pointed out the feasibility and
efficiency of the event-driven sampling scheme in network bandwidth improvement with
less degradation of control performance. This is very useful in the realistic applications
where sensor data transmission rate needs to be lowered due to joining of many sensor
nodes or saving power in wireless networks.

iii
Contents


Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1. Problem overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Networked control systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1. Network architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2. Network protocols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Fundamental issues in networked control systems. . . . . . . . . . . . . . . . . . . . .
1.3.1. Network delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2. Data rate constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3. Network bandwidth constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.4. Sampling and quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.5. Data packet dropouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4. Motivation and contributions of thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1. Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2. Previous works. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3. Contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5. Thesis outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2. Event-based sampling and state estimation problem. . . . . . . . . . . . . . . . . . . . .
2.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Event-based sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. State estimation using event-based sampling. . . . . . . . . . . . . . . . . . . . . . . . . .
2.4. Estimation performance analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5. Estimation performance of the multirate filter. . . . . . . . . . . . . . . . . . . . . . . . .
2.6. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. State estimation for networked monitoring systems. . . . . . . . . . . . . . . . . . . . .
3.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Problem formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ii
iii
1
1
2
3
3
5
5
6
7
7
8
9
9
10
11
11
13

13
13
14
16
17
19
21
22
22
23

iv
3.3. Send-on-delta based state estimation for multi-output systems. . . . . . . . . . . .
3.4. Optimal δ
i
computing problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5. Numerical and experimental simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6. Experimental results over ZigBee network. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Controller design for networked control systems. . . . . . . . . . . . . . . . . . . . . . .
4.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Problem formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Send-on-delta multirate controller design. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1. SOD estimator design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2. SOD multirate controller design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3. Optimal δ
i
computing problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4. Stability of the SOD multirate controller. . . . . . . . . . . . . . . . . . . . . . . .
4.4. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Networked estimation with an area-triggered transmission method. . . . . . . .
5.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Area-triggered sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1. Effect of noise on sensor data transmission rate. . . . . . . . . . . . . . . . . .
5.2.2. Π
i
computation and SOA sampling in discrete time. . . . . . . . . . . . . . .
5.2.3. Effect of noise on signal distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3. State estimation with SOA transmission method. . . . . . . . . . . . . . . . . . . . . . .
5.3.1. Bound of Δ
i
(t, t
last,i
). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2. State estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Networked estimation with packet dropouts. . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. Effect of packet dropouts on system performance . . . . . . . . . . . . . . . . . . . . .
6.2.1. Estimation performance of multirate filter with packet dropouts. . . .
6.2.2. Estimation performance of the SOD filter with packet dropouts. . . . . .
6.2.3. Evaluation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3. Modified SOD sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
25
27
32
34

35
35
36
38
38
39
39
41
43
46
47
47
48
49
51
52
55
56
57
58
61
62
62
63
63
64
64
65

v

6.4. State estimation with modified SOD transmission method. . . . . . . . . . . . . . .
6.4.1. Measurement noise increased due to multiple packet dropouts. . . . . . .
6.4.2. State estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Optimal δ
t,i
computing problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1. Sensor data transmission rate by condition (6.8b) . . . . . . . . . . . . . . . .
6.5.2. Estimation error covariance due to packet dropouts. . . . . . . . . . . . . . .
6.5.3. Optimal
δ
t,i
computation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6. Simulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1. Case 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2. Case 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7. Conclusions and future work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2. Future work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
69
69
71
71
71
72
73
73
77

79
80
80
81
83

















vi
List of Figures


1.1. A control system with a traditional wiring configuration. . . . . . . . . . . . . . . . . . .
1.2. A control system with an NCS configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. A compact NCS configuration used throughout the thesis. . . . . . . . . . . . . . . . . .
1.4. Configuration of an NCS with delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1. Event-based sampling scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Structure of the event-based Kalman filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Error covariance of two filters under the same bandwidth conditions. . . . . . . . .
2.4. P
k
value of two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5. Estimation error of two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1. Structure of the event-based Kalman filter for the multi-out systems . . . . . . . . .
3.2. Experimental of the state estimation system through a CAN bus. . . . . . . . . . . . .
3.3. The relationship between number of sensor data transmissions and s
i
/δ
i
. . . . . .
3.4. Estimation error: standard KF, proposed SOD KF, naive SOD KF. . . . . . . . . . .
3.5. Experiment of the state estimation system through ZigBee network. . . . . . . . . .
3.6. Estimation error: standard KF, proposed SOD KF, naive SOD KF. . . . . . . . . .
4.1. Configuration of a networked control system. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Block diagram of a multirate control system . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Estimation error in 3 methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Step response with initial position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. a. SOD sampling scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. b. SOA sampling scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Sensor output with noise in discrete time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3. Effect of R on data transmission rate and distortion for y
1
. . . . . . . . . . . . . . . . .
5.4. Effect of R on data transmission rate and distortion for y
2
. . . . . . . . . . . . . . . .

5.5. Structure of the modified Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6. Estimation error in case 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7. Estimation error in case 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1. Error covariance without packet loss in two sampling schemes. . . . . . . . . . . . . .
6.2. Error covariance increased due to packet loss in two sampling schemes. . . . . . .
1
2
2
6
14
16
19
20
20
25
28
29
31
32
33
36
37
45
45
49
49
51
53
54
57

60
60
65
65

vii
6.3. a. Principle of conventional SOD sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3. b. Principle of modified SOD sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Multiple packet dropouts detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Measurement noise increased due to multiple packet dropouts . . . . . . . . . . . . . .
6.6. Structure of the modified Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7. δ
t,1
of (6.17) along with δ
y,1
and ξ
1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.
δ
t,2
of (6.17) along with δ
y,2
and ξ
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9. Estimation error in two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10. Instants the sensor node transmits data due to condition (6.8b). . . . . . . . . . . . . .
6.11. Estimation error in two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12. Instants the sensor node transmits data due to condition (6.8b). . . . . . . . . . . . . .

7.1. The modified Extended Kalman filter for nonlinear systems. . . . . . . . . . . . . . . .
66
66
67
69
70
74
74
76
76
78
78
82















viii

ix
List of Tables


2.1. Error covariance in two sampling schemes with different values r and δ. . . . . .
3.1. Numerical results with different estimation performance constraints . . . . . . . . .
3.2. Numerical results in ZigBee network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1. Control performance of the standard controller . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Control performance of the proposed controller. . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Control performance of the multirate controller. . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. Estimation performance of 2 methods with different threshold values in case 1.
5.2. Estimation performance of 2 methods with different threshold values in case 2.
6.1. Estimation error for case 1 in two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. Estimation error for case 2 in two filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
31
33
44
44
44
59
59
75
77

Chapter 1
Introduction


1.1. Problem Overview

In the last two decades, advances in communication, control, and computation
technologies have motivated the rise of a modern control system architecture in which
sensors and actuators exchange information with a feedback controller through a shared
communication medium. Control systems having this configuration have been termed
Networked Control Systems (NCSs). Compared to conventional system architectures, the
advantages of NCSs include reduced system wiring, ease of diagnosis and maintenance,
low cost, and increased system flexibility.
The rise of NCSs stems in part from necessity. Traditionally, control systems have
been implemented using point-to-point wiring, i.e., each sensor and actuator is connected
to a centralized controller (often a micro-processor) via a designated wire (Fig.1.1). This
configuration ensures real-time communication between components of a control system.
However, as the complexity and scale of a control system increase, point-to-point wiring
becomes cumbersome or impractical: the increased wiring burden brings problems
involving weight, cost, maintenance, and reliability. At the same time, the microprocessor
in which the controller is implemented provides a limited number of input/output (I/O)
ports and limited computing capability, so that point-to-point wiring becomes impossible
when the number of sensors and actuators is greater than the number of I/O ports or when
the computation load needed exceeds the capability of the processor.

PLANT
Sensor
1
Sensor
p
Actuator
1
. . . .
Controller
Actuator
q

. . . .

Figure 1.1. A control system with a traditional wiring configuration

1
In an NCS (Fig.1.2), the controller is connected to a communication medium that
provides access to all the sensors and actuators; the medium is shared by all its users, so
that only a limited number of connections can be supported simultaneously. The NCS
configuration has proved remarkably flexible, enabling many novel features in feedback
control systems. For example, using wireless communication, sensors and actuators in an
NCS can easily change their locations to form different ad hoc groups that are customized
for different tasks.

PLANT
Sensor
node 1
Sensor
node p
Actuator
node 1
. . . .
Controller node 1
Actuator
node q
. . . .
Shared communication network
Controller node r
. . . .

Figure 1.2. A control system with an NCS configuration: sensors and actuators

are connected to the controllers via a shared communication network

In this thesis, the configuration of NCS is limited to a compact system as illustrated
in Fig.1.3, where the plant is an SIMO system and only one controller/estimator node is
connected to the network. All sensor nodes are connected to the controller/estimator node
by a serial network for state estimation and control.

PLANT
Controller/
Estimator node
Serial Network
Sensor
node 1
Sensor
node p
Actuator
node
. . . .
1
()
y
t
()
p
y
t
()ut

Figure 1.3. A compact NCS configuration used throughout the thesis

1.2. Networked control systems

2
1.2.1. Network architecture
Consider a typical network architecture in a modern manufacturing system shown
in Figure 1.2. The shared communication network architecture has three different levels,
namely, the Information/System (IS) network, the Discrete-Event/Cell (DEC) network, and
the Continuous-Variable/Device (CVD) network. This classification is based on the
functionality as well as signal characteristics in typical industrial applications.
The top level IS network is used to carry non-time-critical information such as
daily or hourly production data, and to communicate with factory-wide databases.
Messages on an IS network typically have a large data size but low frequency.
The middle level is the DEC network, which carries commands or updated working
configurations for different cells or subsystems. Generally, the messages in a DEC network
are discrete and event-based. The DEC network messages may be periodic, sporadic, or
time-critical. When timing is critical, large time delays and lost data at this level may cause
coordination problems between different subsystems. The analysis and control of DEC
network systems such as manufacturing systems and multi-task robotic systems has been
studied using discrete-event system techniques such as finite state machines, with or
without timing parameters [1], [2].
The bottom level is the CVD network, which communicates physical signals such
as position, velocity, and temperature by the means of network coding and messaging.
Sensors, actuators, and controllers are the types of devices interconnected by CVD
networks. Messages are transmitted periodically and in real-time; data sizes are small, but
message frequency may be high. Time delays and lost data at this level may degrade the
system performance and even cause system instability [3], [4]. The three levels of
networks are separated because they require different information characteristics and
functionalities, although they may be connected by gateways or bridges.
If the same network is used for multiple levels, the large-size data packets
transmitted at the IS-network level could degrade network efficiency in both CVD and

DEC networks, and the high-frequency data packets at the CVD-network level might
further delay the message transmission in either the DEC or IS networks.

1.2.2. Network protocols
Based on the time-delay characteristics of control networks installed in industrial
automation systems, we classify these networks into three types: stochastic, bounded, and

3
constant. This classification focuses on the medium access control (MAC) mechanism and
the time delay between two devices. In this section, we first describe different types of
message connections and then discuss how the MAC determines the time delay
characteristics for three types of control networks: Ethernet-based (stochastic), token-
passing (bounded), and CAN-based (constant).
The three types of control networks commonly implemented in industry are
Ethernet based, token-passing, and CAN-based networks. Ethernet (IEEE 802.3) is a
CSMA/CD (Carrier Sense Multiple Access with Collision Detection) network protocol.
Simply speaking, CSMA/CD specifies that every node should detect the network
availability before sending out messages and, if there are message collisions, a collided
node stops transmitting and waits a random length of time to retransmit messages. Hence,
due to the random binary exponential backoff (BEB) algorithm the transmission delays are
non-deterministic. Although there exist modifications to Ethernet, for example, switched
Ethernet, which seeks to reduce the collision possibility and improve the determinism of
the network, the time delay between two devices is inherently stochastic if the BEB
algorithm is applied.
A token-passing network has bounded time delays. As the name suggests, there is
one token passing around the network and only the device with the token can transmit
messages. Transmission bandwidth is thus divided between all devices although there is
some overhead associated with passing the token. If the network is not saturated, the
message time delay will be bounded; the magnitude of these delays depends on the data
rate, the total number of devices on the network, message size, and maximum token

holding time. Typical examples of token-passing control networks are ControlNet [5],
MAP (IEEE 802.4), and Profibus [6].
CAN-based network (Control Area Network) protocols are optimized for short
messages, and utilize a CSMA/AMP (Carrier Sense Multiple Access with Arbitration on
Message Priority) media access method. Thus, the protocol is message oriented and each
message has a specific priority which is used to determine access to the bus in case of
simultaneous transmission. The bit-stream of a transmission is synchronized on the start bit
and the arbitration is performed on the following message identifier where a logic '0' is
dominant over a logic '1'. Hence, if two devices want to send messages at the same time,
they first continue to send the message frames and then listen to the network. If one of
them receives a bit different from the one it sends out, it loses the right to send its message

4
and the other wins the arbitration. With this method, an ongoing transmission is never
corrupted. Any node that wants to transmit a message waits until the bus is free and then
starts to send the identifier of its message bit by bit. If the message periods and releasing
times are known, the time delays between any two devices can be predetermined and may
be constant. CAN-based networks include DeviceNet [7] and Smart Distributed System
[8].

1.3. Fundamental issues in NCSs
Despite its flexibility and effectiveness, the NCS architecture also introduces new
problems which have been beyond the scope of traditional control systems theory until
recently. In this section, we will briefly analyze some basic problems in NCSs, including
network-induced delay, network scheduling, data rate constraints, sampling and
quantization, and network packet dropouts.

1.3.1. Network delays
The network-induced delay in NCSs occurs when sensors, actuators, and
controllers exchange data across the network. This delay can degrade the performance of

control system designed without considering it and can even destabilize the system.
Packet on random access networks are affected by random delays, and the worst-
case transmission time of a packet is unbounded. Therefore, CSMA networks are generally
considered non-deterministic. However, if network messages are prioritized, higher-
priority messages have a better chance for timely transmission (such as CAN and
DeviceNet).
On scheduling networks, packet transmission delays occur while waiting for the
token or time slot. They can be made both bounded and constant by transmitting packets
periodically. The effects of all these delay components can be typically captured by the
sensor-to-controller delay
s
c
τ
and the controller-to-actuator delay
ca
τ
(Fig. 1.4).
In state-space models, time delays in the feedback loop of a control system can be
effectively captured by introducing additional states to keep track of the delayed
information. This technique is often termed “state augmentation” (also known as “state
lifting” or “state extensification”). For example, it is shown that [9], for a sampled-data
control systems with constant feedback and a sample period h, a constant delay τ of
(r − 1)h < τ < rh (where r ∈ N) will increase the system order by a factor of r. For scalar

5
linear systems, the relationship between the sampling period and allowable time delay can
be illustrated by a stability region plot [10], which can be obtained via analytical or
numerical methods.
Actuator
node

PLANT
Sensor
node
Controller
node
Serial Network
ca
τ
()ut
s
c
τ
c
τ
()
y
t
T

Figure 1.4. Configuration of an NCS with delays

Bounded time-varying delays in a control system’s feedback loop can also be
modeled by proper state augmentation to include the plant’s state and all the delayed
control information; the detail of this technique is illustrated in [10] and [11]. Also using
the augmented state model, some stability and performance analysis tools are given in [12]
for MIMO systems having multiple time delays in different feedback loops. In [13], an
LQR optimal control problem is formulated and studied based on the same model.

1.3.2. Data rate constraints
Communication constraints also manifest themselves in the form of data rate limits

on the communication medium. The effects of data rate limits on networked control
systems have typically been studied from information theoretic perspectives, and the
communication medium is often modeled as a coded channel with a bandwidth limit.
The work in [14] investigates state estimation in NCSs where the observations are
transmitted to an estimator with a finite data rate. The authors introduce a recursive coder-
estimator scheme, in which the coding decision can be dependent on the whole past history
of the observation process, and the estimator can be dependent on the whole sequence of
past codewords. Necessary and sufficient conditions are established for the existence of
stable and asymptotically convergent coder-estimator schemes. Under the coder-estimator
framework, feedback stabilization under data rate constraint is investigated in [15]. It is
shown that, if the plant is a continuous-time LTI system, then memoryless coding and

6
control suffice to ensure the containability of the system, meaning that given small enough
initial conditions, the trajectory of the system will lie in an n-dimensional sphere of an
arbitrary size.
The work in [16] investigates the stability of infinite-dimensional linear discrete-
time plant when the controller receives observation data at a known rate. It is shown that,
under a finite horizon cost equal to the m-th output moment, the problem reduces to
quantizing the initial output. As the horizon approaches infinity, asymptotic quantization
theory can be applied to directly obtain the limiting coding and control scheme. Necessary
and sufficient conditions can then be derived for the system to be asymptotically
stabilizable in the m-th moment at a given data rate. Under some restrictions on the initial
condition distribution, a coding-estimation scheme is presented in [17]; this scheme works
for finite dimensional, time-varying nonlinear system that satisfies a Lipschitz-type
condition.

1.3.3. Network bandwidth constraints
One of the fundamental communication constraints in a communication network is
medium access. It comes about because a communication bandwidth can only provide

limited number of simultaneous medium access channels for its users. As a consequence,
in an NCS, only limited number of sensors and actuators are allowed to communicate with
the controller at any one time.
In modern communication networks, medium access constraints are often resolved
via various Medium Access Control (MAC) protocols which define the access scheduling
and collision arbitration policies in the network. MAC protocols can be roughly divided
into two categories, namely sequential MAC protocols and random MAC protocols. Under
sequential MAC protocols, each user of the network accesses the shared medium according
to a pre-configured sequence. Under random MAC protocols, every user attempts to access
the media whenever it has a packet to transmit; if there are other users wanting to access
the medium at the same moment, an arbitration policy is used to resolve the packet
collision.

1.3.4. Sampling and quantization
Sampling schemes can either be time-driven or event-driven. Astrom and
Bernhardsson [18] compared the merits of the Riemann sampling (time-driven) and the

7
Lebesgue sampling (event-driven) for one-dimensional systems. Yook et al. [19] proposed
that a node should broadcast the true value of the local plant state when it differs from the
estimate known to the remote nodes by more than a given threshold. They show that this
scheme results in a system that is bounded-input bounded-output stable. The relation
between the threshold level and the message exchange rate is investigated through
simulations.
A signal has to be quantized before being encoded and sent to a digital channel. A
quantizer is a device that converts real numbers (an analog signal) into a finite set of
integers (a digital signal). Mathematically, a quantizer is a piecewise constant function,
mapping a quantization region to a quantization point. Usually, a quantization region is a
pre-specified rectangular shape. More efficient quantization schemes (for controls) have
been developed over the years. Both [20] and [21] advocate logarithmic-based quantization

methods. Roughly speaking, quantization region becomes larger logarithmically as the
distance from the origin grows. Quantization regions are allowed to evolve with time to
capture the system dynamics [22].

1.3.5. Data packet dropouts
Dropping network packet occasionally happens on an NCS when there are node
failures or message collisions. Although most network protocols are equipped with
transmission-retry mechanisms, they can only re-transmit for a limited time. After this time
has expired, the packets are dropped. Furthermore, for real-time feedback control data such
as sensor measurement and calculated control signals, it may be advantageous to discard
the old, untransmitted message and transmit a new packet if it becomes available. In this
way, the controller always receives fresh data for control calculation.
Normally, feedback-controlled plants can tolerate a certain amount of data loss, but
it is valuable to determine whether the system is stable when only transmitting the packets
at a certain rate, and to compute acceptable lower bounds on the packet transmission rate.
In [10], it is shown that an NCS with data packet dropout can be modeled as an
asynchronous dynamical system (ADS) with rate constraints on events [23]. Using that
model, one can calculate the minimum transmission rate that guarantees the stability of an
NCS whose closed-loop dynamics are stable without the presence of packet dropout.
Another possibility for addressing dropped data packets is to model the arrival of data as a
random process. For example, the work in [24] studies state estimation of SISO NCSs, in

8
which scalar observations arrive according to a Poisson process; the work in [25] presents
a Kalman Filter scheme for MIMO systems in which the arrival of output information (all
outputs as packets) is modeled as a Bernoulli process. These works are generalized in [26]
where outputs are divided into two parts each of which can be received or lost by the
Kalman Filter independently.
In a very recent study [27], the optimal H
2

filtering problems associated
respectively with possible delay of one sampling period, uncertain observations and
multiple packet dropouts are studied under a unified framework. The H
2
-norm of systems
with stochastic parameters is defined and computed via a Lyapunov equation and a steady-
state filter is designed via an LMI approach. The authors modeled the multiple packet
dropout case, where the random dropout rate is transformed into a stochastic parameter in
the system’s representation.

1.4. Motivation and contributions of thesis
1.4.1. Motivation
A major trend in modern industrial and commercial systems is to integrate
computing, communication, and control into different levels of machine/factory operations
and information processes. The traditional communication architecture for control systems,
which has been successfully implemented in industry for decades, is point-to-point, that is,
a wire connects the central control computer with each sensor or actuator point. However,
expanding physical setups and functionality are pushing the limits of the point-to-point
architecture. Hence, a traditional centralized point-to-point control system is no longer
suitable to meet new requirements, such as modularity, decentralization of control,
integrated diagnostics, quick and easy maintenance, and low cost. The introduction of
common-bus network architectures can improve the efficiency, flexibility and reliability of
these integrated applications, and reduce installation, reconfiguration, maintenance time
and costs.
The change of communication architecture from point-to-point to common-bus,
however, introduces several issues as mentioned in Section 1.3. Most NCS research has
dealt with the issues: network-induced delay, network constraints, and packet dropouts.
When several nodes are connected to the network, network-induced delay is inevitable. It
is well-known in control systems that time delays can degrade the system's performance
and even cause system instability.

9
This dissertation focuses on the issue of signal sampling scheme and data
transmission method in order to reduce data transmission rate on the network. If the
transmission rate is low, it is clearly that network-induced delay is also small and can be
ignored in some certain cases. Therefore, the problem of estimation and control over
networks becomes easier to deal with when ignoring network delay.

1.4.2. Previous works
The traditional way to design networked control systems is to sample the signals
equidistant in time. A nice feature of this approach is that analysis and design becomes
very simple. For linear time-invariant processes the closed loop system becomes linear and
periodic. But, the periodic sampling scheme introduces large data transmission rate over
network because the sensor nodes have to send data every sampling time.
Event-based sampling scheme, also called level-triggered sampling, level-crossing
sampling, send-on-delta, deadband, or Lebesgue sampling, samples the signal when its
output has changed with a specified amount. A disadvantage of this sampling scheme is
that analysis and design are complicated. Therefore, it has not received much attention
although much work on systems of this type was done in the period 1960-1980.
However, recent works have discussed event-driven alternatives to traditional time-
triggered sampling scheme. It has been shown to be more efficient than time-triggered one
in some situations, especially in network bandwidth improvement. We will review a
number of previous researches here to understand the related work.
• In [18], the authors provided a comparison of time-triggered impulse control and
level-triggered one where the level-triggered scheme gave lower average error for the
same average rate of impulse.
• In [28][29], an adjustable deadband was defined on each node to reduce network
traffic. The node does not broadcast a new message if its signal is within the
deadband. A method to determine the size of the deadbands was presented that relies
on a performance metric that takes into account system response as well as network

traffic.
• In [30], the authors introduced the use of a level-crossing sampling scheme based on
hysteretic quantization for feedback stabilization under data-rate constraints.
Hysteresis allows us to implement 1-bit coding feedback communication which has
the potential to achieve the most efficient data-rates. In addition, under noisy

10
scenarios, hysteresis would also minimize spurious sampling, further contributing to
low data-rate feedback communication. This coding sampling scheme becomes
highly efficient under data-rate constraints since the nodes only transmit one bit, 0 or
1, per sample.
• The work [31][32] solved an optimal level-triggered sampling design problem in
which the distortion of a filter is minimized over a finite horizon. A method for
designing good level-triggered control schemes was obtained by reducing the
continuous time problem to discrete time. Then, by numerical procedures, the
performance of the level-triggered scheme is computed for comparison with that of
the periodically switched control scheme.
• In [33][34][35], where the event-based sampling has the name of send-on-delta
method, the authors presented the analytical method for estimation of the mean
sampling rate and sampling effectiveness defined as a ratio of the number of samples
taken in periodic and event-based schemes.

1.4.3. Contributions
Motivated by the perspective results of the event-based sampling in [28-35], the
aim of this thesis is to explore the problem of estimation and control over networks using
event-based transmission method. We address the following problems:
• Derive formulation for the problem of state estimation and optimal LQG control
when the sensor nodes are sampled by the event-based method.
• Find the optimal threshold value at each sensor node such that the overall sensor data
transmission rate is minimized and the degradation of control performance is small.

• Consider the impact of packet dropouts on system performance and propose a novel
event-based sampling scheme to improve system performance.

1.5. Thesis outline
Chapter 2: we introduce the event-based sampling scheme in which sensor data are
transmitted to the estimator node only if the difference between the current sensor value
and the last transmitted one is greater than a given threshold. We compare the event-based
sampling with the multi-rate sampling to evaluate the system performance as well as
network traffic.

11

12
Chapter 3: We formulate the state estimation problem for the linear systems when
the sensor nodes are sampled by the event-based method. Then we derive the optimization
problem to find the optimal threshold value at each sensor node. The threshold value is a
trade-off parameter between the overall sensor data transmission rate and the estimation
performance. If the threshold value is large, the sensor data transmission rate is small
(improve network bandwidth) but estimation performance degrades much. Otherwise, if
the threshold value is small, the estimation performance is good but sensor data
transmission rate is increased (network traffic is high).
Chapter 4: An optimal LQG controller is designed for the NCS in which sensor
data are sent to the controller node with the event-based method, and the controller node
send data to the actuator node periodically. We prove the stability of the proposed
controller and show that control performance of the proposed controller is better than that
of the multirate controller.
Chapter 5: We propose a novel even-based sampling scheme to improve system
performance. The conventional event-based sampling scheme has some flaws that degrade
system performance. For instance, the transmission rate of the even-based method becomes
large when the sensor noise is large. Furthermore, it does not detect signal oscillations or

steady-state error if the signal variation remains within the threshold range during a long
time.
Chapter 6: The impact of packet dropouts on system performance is considered and
evaluated. Then a modified estimator is formulated in the case of multiple packet dropouts.
Chapter 7: We summarize the contributions of the thesis and discuss the possibility
of future works.
Chapter 2
Event-based sampling and state estimation problem


2.1. Introduction
In this chapter, we will introduce an overview of event-based sampling scheme ( or
called send-on-delta sampling scheme) and its advantages in network bandwidth
improvement. A modified Kalman filter is proposed to evaluate estimation performance of
the systems using event-based sampling.
We also introduce a multi-rate sampling scheme, in which the output signal is
sampled by the time-triggered scheme, in order to compare system performance as well as
data transmission rate in two sampling schemes.

2.2. Event-based sampling scheme
Consider a networked monitoring system (Fig 1.3) described by the linear
continuous-time model:
() () ()
() () ()
xt Axt wt
yt Cxt vt
=+
=+

(2.1)

where is the scalar state of the plant, y is the measurement output which is
sent to the estimator node by the sensor node. is the process noise with covariance
, and is the measurement noise with covariance R .
xR∈
()vt
R∈
()wt
Q
In this chapter, we only consider a scalar system for simplicity in problem
formulation. The multi-output system is considered in the next chapters. The output signal
of the system (2.1) is sampled by an event-based scheme as depicted in Fig.2.1, where
the slash line presents measurement output value at the sensor node and the solid line
presents the sensor data value received at the estimator node.
()yt
(
last
y
()yt
)t
The principle of sampling and transmitting the output signal is described as
follows:
()yt
i) Let
last
y be the latest output value that the sensor node sent to the estimator
node at time
last
t .
ii) The next sensor value of
()yt will be transmitted to the estimator node only if:

13