Stabilization of networked control systems via
controller and protocol co-design
Hongbo Song
Department of Computer Sciences
Zhejiang University of Finances & Economy
Hangzhou, China, P.R. China
di7ganshb@163.com
Zhen Hong
Faculty of Mechanical Engineering & Automation
Zhejiang Sci-Tech University
Hangzhou, Zhejiang, P.R. China
zhong@zstu.edu.cn
Abstract—This paper studies the stabilization for networked
control systems with medium access constraint via controller and
protocol co-design. The closed-loop networked control system is
modeled as a discrete-time switched system. Sufficient conditions
are presented for the exponential stability of the closed-loop
networked control system by the average dwell time method.
Based on the conditions, stabilizing controllers and the
scheduling protocols are designed. Finally a numerical example is
employed to demonstrate the effectiveness of the proposed
method.
Keywords—networked control systems; medium access
constraint; co-design; stabilizing controller; protocol
I. INTRODUCTION
In the past decade, the modeling, analysis and synthesis of
networked control systems (NCSs) have attracted much
research interests since NCSs bring many advantages, such as
reduced cost, simple installation and maintenance, and high
reliability [1-3]. However, the presence of the network in the
closed loop introduces many challenging problems such as
network-induced delays, packet-dropouts and medium access
constraints. The delay and packet-dropout issues have
appeared to be hot research topics, see [4-6] for example and
the references therein. However, much fewer results are
available on the medium access constraints issue, which is an
important researching field needs investigation [7-9].
In an NCS, only a limited number of sensors and actuators
are allowed to communicate with the controller at one time
and this issue is called the medium access constraints [9].
Thus scheduling protocols are needed to allocate the limited
access resources to the sensors and actuators. The design of
scheduling protocol is very important in NCSs since the
system performance will degrade if scheduling protocols are
not properly chosen. In [7], a protocol called maximum-error-
first with try-once-discard (MEF-TOD) was presented, which
firstly designed a stabilizing controller without taking the
network into consideration and then derived the maximum
allowable transfer interval (MATI) that preserves the stability
of the NCS. However, the obtained result was conservative.
Therefore, many researchers attempt to use alternative
approaches to reduce the conservatism of the MATI result in
[7]. For example,
a new hybrid system model was presented in
[10,11], where the
l
stability of the presented nonlinear
NCSs was studied and less conservative MATI results were
obtained based on the small gain theorem. Another efficient
way to deal with the NCSs with medium access constraints is
to co-design the controller and the protocol with fixed transfer
interval, such as that in [12-14]. However, all the
aforementioned results used the zero order holder way to
compensate the sensors and the actuators which are not
communicating with the controller. In [9], a different way
called setting zero was developed for the NCSs with medium
access constraints. The method ignores the effects of the
sensors and the actuators that are not actively communicating.
The main advantage of the treatment is the degradation of the
complexity in the analysis and synthesis of the NCS. In [15],
the effects of using zero order holder and setting zero schemes
were studied for NCS and the results showed that no one is
superior to the other for the studied cases. In [16], the
H
f
control problem was studied by using the setting zero scheme
of NCSs with medium access constraints and packet dropouts.
In this paper, the stabilization of NCS via controller and
protocol co-design based on the modeling method in [9]. By
considering the state feedback controllers, the closed-loop NCS
is modeled as a discrete-time switched system. The average
dwell time method is proposed to derive the exponential
stability criteria for the obtained closed-loop NCS.
Furthermore, co-design procedures for the stabilizing controller
and the scheduling protocol are presented based on the
obtained stability criteria. Finally, an illustrative example is
given to demonstrate the effectiveness of the proposed results.
II.
MODELING OF CLOSED-LOOP NCS
The structure of the considered NCSs is shown in Fig.1
and the pant to be controlled is represented by the following
linear system model:
ˆ
() () ()
pp
tAxtBut
(1)
where
1
[]
Tn
n
xxR " is the plant state,
1
ˆˆ ˆ
[]
Tm
m
uu u R "
is the control input,
i
and
ˆ
j
u
,
{1, 2 , , } , {1, 2 , , }iN njM m "", are scalars. The
plant state
i
is measured by the sensor
i
and the control
input
ˆ
j
u
is received by actuator
. All the sensors and
actuators are communicating with the controller every
constant interval
T
.
This research work was supported by the National Nature Science
Foundation of China (No. 61304040) and the Nature Science Foundation o
Zhejiang Province (No. LQ13F030005).
934
2014 International Conference on Mechatronics and Control (ICMC)
July 3 - 5, 2014, Jinzhou, China
978-1-4799-2538-4/14/$31.00 ©2014 IEEE