A novel approach for internet congestion control using an extended state observer 2

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
INTERNATIONAL JOURNAL OF ELECTRONICS AND
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 2, March – April, 2013, pp. 80-92
IJECET
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2013): 5.8896 (Calculated by GISI) ©IAEME
www.jifactor.com

A NOVEL APPROACH FOR INTERNET CONGESTION CONTROL
USING AN EXTENDED STATE OBSERVER

Kaliprasad A. Mahapatro1, MilindE.Rane2
1,2
Department of Electronics and Telecommunication Engineering, Vishwakarma
Institute of Technology, Pune- 411019 INDIA

ABSTRACT

Congestion is the key factor in performance degradation of the computer networks
and thus the congestion control became one of the fundamental issues in computer networks.
Congestion control is the mechanism to prevent the performance degradation of the network
due to changes in the traffic load in the network. Without proper congestion control
mechanisms there is the possibility of inefficient utilization of resources, ultimately leading
to network collapse. Hence congestion control is an effort to adapt the performance of a
network to changes in the traffic load without adversely affecting user’s perceived utilities.
This paper present the novel approach for internet congestion control using an
Extended State Observer(ESO) along with the proportional-derivative(PD) Control, which
improve the performance of congestion control on TCP/IP networks by estimating the
uncertainties and disturbances, in the network.
This paper also discusses the limitation of some classical observer like Disturbance
Observer (DO) and how it is overcome by ESO by extending idea to practical non-linear
system. The simulation shows that, the extended state observer is much superior in dealing
with dynamic uncertainties and variation in network parameter.

Index Terms: TCP/IP, Disturbance Observer (DO), Extended State Observer (ESO),
Proportional-Derivative (PD).

I. INTRODUCTION

Traditionally the Internet has adopted a best effort policy while relying on an end-to-
end mechanism. Complex functions are implemented by end users, keeping the core routers
of network simple and scalable. This policy also helps in updating the software at the users
end. Thus, currently most of the functionality of the current Internet lay within the end users
protocols, particularly within Transmission Control Protocol (TCP). This strategy has worked
80


fine to date, but networks have evolved and the traffic volume has increased many folds;
hence routers need to be involved in congestion control, particularly during the period of
heavy traffic. A conventional design approach by implementing multi path Energy Efficient
Congestion Control Scheme to reduce the packet loss due to congestion have been carried out
in [1] by combining congestion estimation technique by taking into account queue size,
contention and traffic rate. But due to this open-loop technique an efficient control cannot be
carried out.
In order to find effective solutions to congestion control, many feedback control
system models of computer networks have been proposed. The closed loop formed by
TCP/IP between the end hosts, through intermediate routers, relies on implicit feedback of
congestion information through returning acknowledgements. Active Queue Management
(AQM) scheme have been proposed in recent years [2]. Two types of methodologies to deal
these issues are congestion control and congestion avoidance. In this we will deal with
congestion control because it helps in the reactive planning by applying feedback technique.
A more well-known AQM scheme is probably Random Early Detection [3]. RED can detect
and respond to long-term traffic patterns, but it cannot detect the short-term traffic load. [4],
in most of the cases parameter adjustment in RED are performed by using heuristic function
because of which the probability to determine uncertainties and disturbances in network
parameters reduces. To overcome above mentioned flaws [5] shown that a proportional
controller plus a Smith predictor provides an exact model of the Internet flow and congestion
control with a guaranteed stability and efficient congestion control. Active queue
management (AQM) scheme based on a fuzzy controller, called hybrid fuzzy-PID controller
[6] shows that, the new hybrid fuzzy PID controller provides better performance than random
early detection (RED) and PID controllers. To improve the performance even better a robust
2-DOF PID control was implemented in [4] for better congestion control. A linear gain
scheduling by using PID as given by T.Alvarez in [7]stability region was well explained by
using Hobenbichlers approach.
In meanwhile a well-known classical observer known as Disturbance Observer(DOB)
was introduced in [8] with an artificial delay, but DOB can only work efficiently with an
ideal assumption of slow varying noise or constant disturbances i.e. d_ = 0, which is well
explained in the following section III.
From the aforementioned flaws in various mechanisms, a novel AQM scheme that
supports TCP flows and avoids drastic congestion due uncertainties and disturbances in
network parameter is introducing a modern observer known as extended state observer
(ESO). ESO was carried out in various sensitive plant like nuclear-reactor, space application
like NASA’s flywheel [9] etc. because of its beauty controlling internal dynamics and
external disturbances of a non-linear plant from its input-output data. Continuing the same
this paper approaches to solution of estimating disturbances in network parameter by using
ESO.
The composition of this paper is as follows. Section II presents the non-linear
modeling of TCP/IP protocol. Section III briefly describes the limitation of disturbance
observer. Section IV describes the mathematical approach of non-linear extended state
observer with its control parameter for calculating uncertainties and simulation of the same is
carried out. Extending the idea of section IV a robust control is demonstrated in Section V by
introducing feedback control i.e. ESO+PD. Finally conclusion is stated in Section VI.

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II. TCP/AQM ROUTER DYNAMIC MODEL

In this section we will be briefly discuss about the proposed non-linear model of
TCP/IP protocol and linearizing the same for controller design.

A. Nonlinear model

As in the literature, a nonlinear model of TCP/AQM [10] [8] of a single congested router
with a transmission capacity C is given as

ሶ ‫݌‬൫‫ ݐ‬െ ܴሺ‫ ݐ‬ሻ൯ ൅ ோሺ௧ሻ
ௐቀ௧ିோ൫௧ିோሺ௧ሻ൯ቁ
ܹሺ‫ݐ‬ሻ ൌ െ
ௐሺ௧ሻ ଵ
ଶ ோ൫௧ିோሺ௧ሻ൯
(1)

ܹሺ‫ݐ‬ሻ െ ‫ݍ ,ܥ‬ሺ‫ݐ‬ሻ ൐ 0
ேሺ௧ሻ
‫ݍ‬ሺ‫ݐ‬ሻ ൌ ൝ோሺ௧ሻ
ሶ
݉ܽ‫ݍ ,0ݔ‬ሺ‫ݐ‬ሻ ൌ 0
(2)

ഥ
are the positive bounded quantities i.e.,ܹ ‫ א‬ሾ0, ܹ ሿ and ‫ א ݍ‬ሾ0, ‫ݍ‬ሿ. The congestion of window
ത
whereW& q is the maximum window size and average queue length(i.e. buffer size), they

probability p(t) ‫ ]1 ,0[ؠ‬and output is queue velocity‫ݍ‬ሶ _ To linearize equation(1) following
size is increased after every round-trip time R(t). p(.) denotes the (input function) packet drop

assumptions are made[4]

i.e. N (t) ‫ ؠ‬N.
• active TCP session N(t) are time invariant

i.e. C (t) ‫ؠ‬C.
• transmission link capacity are time invariant

• time delay argument ‫ ݐ‬െ ܴon queue length q is assumed to be fixed to ‫ ݐ‬െ ܴ଴ then
the linearize model of equation(1) results into

ሶ
ߜܹ ሺ‫ݐ‬ሻ ൌ െ ோమ஼ ൫ߜܹ ሺ‫ݐ‬ሻ ൅ ߜܹ ሺ‫ ݐ‬െ ܴ଴ ሻ൯ െ ோమ ஼ ൫ߜ‫ݍ‬ሺ‫ ݐ‬ሻ ൅ ߜ‫ ݍ‬ሺ‫ ݐ‬െ ܴ଴ ሻ൯ െ ଶேమ ߜ‫ݍ‬ሺ‫ ݐ‬െ ܴ଴ ሻ (3)
ே ଵ ோబ ஼
మ

బ బ

ߜ‫ݍ‬ሶ ሺ‫ݐ‬ሻ ൌ ߜܹሺ‫ݐ‬ሻ െ ߜ‫ݍ‬ሺ‫ݐ‬ሻ
ே ଵ
ோబ ோబ
(4)

f(ܴ଴ , ܹ଴ , ‫݌‬଴ , ‫ݍ‬଴ ) with a desired equilibrium queue length q0 is given by
where W(t) and _q(t)are the incremental variables w.r.t operating point as a function of

82


ܴ଴ ൌ ൅ ܶ௣
௤బ
‫ۓ‬ ஼
ۖ ܹ଴ ൌ
ோబ ஼
ே
‫۔‬ ‫݌‬଴ ൌ మ
ଶ
(5)
ۖ ௐబ
‫ݍە‬଴ ൌ ‫ݐ݄݈݃݊݁ ݁ݑ݁ݑݍ ݐ݁݃ݎܽݐ‬

This lead to a nominal model, and is given as

Fig. 1. Linearized model of TCP/AQM networks

‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ܲ௧௖௣ ሺ‫ݏ‬ሻܲ௤௨௘௨௘ ሺ‫ݏ‬ሻ݁ ିோబ௦ (6)

where‫ܩ‬ሺ‫ݏ‬ሻ is the transfer function of the plant of TCP/AQM network which includes second-

Where ܲ௧௖௣ ሺ‫ݏ‬ሻ and ܲ ௤௨௘௨௘ ሺ‫ݏ‬ሻ are given as
order system and time delay element as shown in Figure: 1

ೃ೙ ಴ మ

ܲ௧௖௣ ሺ‫ݏ‬ሻ ൌ మಿ೙మ
మಿ೙
௦ା మ
(7)
ೃ೙ ಴

ಿ೙

ܲ௤௨௘௨௘ ሺ‫ݏ‬ሻ ൌ
ೃ೙
భ
௦ା
(8)
ೃ೙

Therefore from equation (7) (8) & figure: 1 ‫ܩ‬ሺ‫ݏ‬ሻ can be stated as

಴మ
‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ܲ଴ ሺ‫ݏ‬ሻ݁ ିோబ ௦
ൌ మಿ
మಿ
భ ݁ ିோబ௦
൬௦ା మ ൰ቀ௦ା ቁ
(9)
ೃబ ಴ ೃబ

by taking network parameter of [4] as C = 3750packets/sec, ‫ݍ‬଴ = 175packets, ܶ௣ = 0:2sec.
In order to illustrate the effectiveness of ESO method, a numerical situation will be presented

For load of N = 60 TCP sessions, ‫݌‬଴ = 0:008& substituting the same in equation (5) we get
ܹ଴ = 15packets, &R ଴ = 0:246.

‫ ܩ‬ሺ‫ݏ‬ሻ ൌ ሺ௦ା଴.ହଷሻሺ௦ାସ.ଵሻ ݁ ି଴.ଶସ଺
ଵ.ଵ଻ଵ଼଻ହൈଵ଴ఱ
(10)

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III. CHEN’S DISTURBANCE OBSERVER

For simplicity of analysis of Disturbance Observer let us consider a linear time-invariant,
continuous-time dynamic system of TCP/AQM in equation (9) model as
.
x = Ax + Bu+Bd (11)

y= Cx (12)
Where, A,B are the nominal system matrices considering no uncertainties and d is a constant or slow
varying input disturbance which is to be estimated.
A. Mathematical modeling
Constant Disturbance
Considering z1 to estimate of d the equation (35 in [11]) can be written as
.
z1 = ξ + c1x 1= &
ξ + c1 x (13)

.
1 = ξ + c1 (Ax +Bu +Bd) ……. from eqn8 (14)
.
Choosing ξ as - c1 (Ax+Bu) - c1Bd and sub in 10 we get.......

1= − c1 (Ax + Bu) − c1Bz1 + c1 (Ax + Bu) + c1Bd (15)

= (d- z1) c1B (16)

whered - z1 disturbance estimation error, denoting the same by η Equation 15 reduces to

1= C1 η ................ where C1 = c1B (17)

Thus, under the assumption that d˙= 0 we can write,

ߟ ൌ െ‫ݖ‬ଵ ൌ െ‫ܥ‬ଵ ߟ
ሶ (18)

ߟ ൅ ‫ܥ‬ଵ ߟ ൌ 0
ሶ ሺ19ሻ
or

C1 ≫ 0 or C1→∞
Thus by the property of linear differential equation If C1>0 thenߟ →0. Thus error→0 as we increases

This is well explained in Figure: 7.

The problem with this observer is that it fails when the assumption of ݀ሶ = 0 is violated. Thus, under
B. Limitation of Disturbance Observer

the assumption that ݀ሶ ് 0 we can write,

ߟ ൌ ݀ሶ െ ‫ݖ‬ଵ
ሶ ሶ (20)

= ݀ሶ െ ‫ܥ‬ଵ η
ሶ (21)

ߟ ൅ ‫ܥ‬ଵ ߟ ൌ ݀ሶ
ሶ
Or
(22)

Thus by the property of linear differential equation ifC1 >0 then ߟ →݀ሶ , which state that error
dynamics never reduces to zero under condition݀ሶ ് 0 which is rather a practical case.

84


IV. NONLINEAR EXTENDED STATE OBSERVER

As seen from previous section the attention was restricted to constant or slow varying
disturbances which never occur or can be achieved practically. Extending the idea to practicalnon-
linear system on of the famous modern observer known as Extended State observer was introduced by
a Chinese scientist J.Han. Extended state observers offer a unique theoretical fascination. The
associated theory is intimately related to the linear as well as non-linear system concepts of
controllability, observability, dynamic response, and stability, and provides a setting[11][12] in which
all of these concepts interact. Extended state Observer can estimate the uncertainties and state of the
plant [13].

A. Mathematical Modeling of ESO
In general the 2nd order non-linear equation is represented as

ÿ = ሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻ+ b0u (23)

Where f (.) represent the dynamics of the
plant+ disturbance,
w- is the unknown disturbance,
u -is the control signal,
y -is the measured output,
b0 -is assumed to be given.
The Equation 19 was augmented as

 x1
& = x2
x
 &2 = x3 + b0 u

&
 x3 =h
y
 = x1
(24)

Here ݂ሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻ and its derivative hൌ ݂ሶሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻare assumed to be unknown, it is now possible to

݂ሺ‫ݕ ,ݕ‬ሶ , ‫ݓ‬ሻby using state estimator for equation 20. HAN proposed a non-linear observer.
estimate

 z1
& = z2 +β1 g1 (e)
z +β2 g2 (e) +b0u
 &2 = z3

 z3 = β3 g3 (e)
&

where e=y-‫ݖ‬ଵ ‫ݖ‬ଷ is the estimate of the uncertain function f (.).
 (25)

݃ଵ (.)is modified exponential function given as......

e ai
sign ( e ) , e > δ
g i (e, ai , δ ) = 
 e
 1-a ,e <δ
 δ i
(26)

ߙ is chosen between 0 & 1
Where.......

݃ଵ is the gain.
•

ߜis the small number used to limit the gain.
•

ߚ is the observer gain
•
•

85


B. State space representation of TCP/IP protocol
As seen from equation (28) &(25)for simplicity in simulation of ESO it is better to represent transfer
function of TCP/AQM plant in the form of state space. Therefore equation (9) can be represented in
the form

‫ ݔ‬ൌ ‫ݔܣ‬ሶ ൅ ‫ݑܤ‬as

‫ݔ‬ሶ 0 1 ‫ݔ‬ଵ 0
൤ ଵ൨ ൌ ቂ ቃ ቂ‫ ݔ‬ቃ ൅ ቂ ቃ‫ݑ‬
‫ݔ‬ሶ ଶ െ2.173 െ4.63 ଶ 133.91 ൈ 10ଷ
(27)

writing Equation (27) in the form (28) we get

‫ݔ‬ሶ ଵ ൌ ‫ݔ‬ଶ
‫ ݔ‬ൌ െ૛. ૚ૠ૜࢞૚ െ ૝. ૟૜࢞૛ ൅ 133.91 ൈ 10ଷ
ሶ
Plant൞ ଶ
‫ݔ‬ሶ ଷ ൌ ݄
(28)
‫ ݕ‬ൌ ‫ݔ‬ଵ

C. Estimation of unknown function
In this section we will estimate the unknown function as stated in equation (28). To make the
simulation more practical we added random number to the o/p of the plant which is treated as noise in
the network parameter.

Fig. 2. Block diagram of ESO for estimation of unknown function in presence of dynamic
noise

86


In figure: 2gives the detail block diagram of estimating state, which is simulated in
SIMULINKMATLAB and resulted are provided in Figure: 3. the profile generator is
taken during the simulation initially as step input. The input is feeded to the usual

The difference of output of the plant ‫ݔ‬ଵ and ‫ݖ‬ଵ which is derived ultimately from ‫ݖ‬ଷ as
ሶ ሶ ሶ
plant and to ESO s as a reference input.

seen from Equation:25 is taken as input by ESO block, together with o/p difference,
input and algorithm proposed in equation:25 & 26 the estimation z3 is carried out and
plotted on scope along with output of plant. The detail description of parameters and
plant and ESO is carried out in following subsection.

D. Adjustment of parameters α, β, δ
Calculation of ߙ
Scale ߙ௜ is chosen in between 0& 1, because it yields ݃௜ high gain [14] [6]. In our case

- ߙଵ = 1.00
we consider for Equation: 26 as.........

-ߙଶ = 0.750
-ߙଷ = 0.625

Calculation of ߚ Gain bi is adjusted by using pole-placement method. In our case by
using matlab simulation by using place (A’ B’ p) command.ߚ௜ for Equation: 25

- ߚଵ = 109
as.........

- ߚଶ = 3858
- ߚଷ = 44640

Calculation of ߜ
ߜis the small number used to limit the gain in the neighborhood of origin. In our case

- ߜ = 10ିଷ
it is taken as for Equation: 26 as.........

25& 26 estimation is carried out in matlab for step in Figure: 3, its seen that ‫ݖ‬ଷ (Z in
Considering values in above subsection and substituting the same in Equation: 28,

Fig) converges to unknown functionf (.).

V. ROBUST CONTROL

Based on their open loop performance, NESO from figure: 1 is evaluated in a

generator provides the desired state trajectory in both y and ‫ ,ݕ‬in simulation we have
ሶ
closed-loop feedback setting, such as that shown in Figure: 4 for NESO. The profile

used step and sine profile. Based on

87


Fig. 3. Estimation of unknown function in presence of dynamic noise

the separation principle, the controller is designed independently(PD block in figure:4),

state information, ‫ݖ‬ଷ , which converges to ‫ݔ‬ଷ ൌ ݂ሺ‫ݓ ,ݕ ,ݕ‬ሻis used to compensate for the
ሶ
assuming that all states are accessible in the control law. In the case of NESO, the extended

unknown ݂ሺ‫ݓ ,ݕ ,ݕ‬ሻ. In particular, the control law is given as
ሶ

‫ݑ‬ൌ
ି௭య ା௄௘
௕బ
(29)

where e = ሾ‫ݒ‬ଵ െ ‫ݖ‬ଵ , ‫ݒ‬ଶ െ ‫ݖ‬ଶ ሿ் and K is the state feedback gain that is equivalent to a
proportional derivative (PD) controller design, and ‫ݒ‬ଵ ൌ ‫ݔ‬ଵ ‫ כ‬and ‫ݒ‬ଶ ൌ ‫ݔ‬ଶ ‫ כ‬where ‫ݔ‬ଵ ‫ כ‬is a plant
i/p as shown in figure:4 Substituting (29) in (23)

‫ݕ‬ሷ ൌ ሺ݂ ሺ‫ݓ ,ݕ ,ݕ‬ሻ െ ‫ݖ‬ଷ ሻ ൅ ‫݁ܭ‬
ሶ (30)

K matrix can be determined via pole-placement [8][15] determining K matrix as

݇ଵ െ10
൤ ൨ൌቂ ቃ
݇ଶ െ05
(31)

88


Fig. 4. Complete Robust control block.

A control o/p of network can be seen in figure: 5 for step input and to explain the beauty of
ESO+PD for compensating o/p, a smooth control o/p can been seen in figure: 6 when sine i/p
is applied and keeping the parameters same as that of step input.

89


Fig. 5. O/p of proposed congestion controller ESO + PD when i/p is step signal

Fig. 6. O/p of proposed congestion controller ESO + PD when i/p is sine wave

90


VI. CONCLUSION

1) As seen from section (III), Disturbance Observer only estimates the disturbances and not

disturbance is not constant i.e. ݀ሶ ് 0. Therefore Disturbance Observer works fails to
thestate of the plant. As seen from equation: 22 DO fail to estimate the disturbances when

worksunder practical application.
2) To overcome the disadvantages of DOB and PID controller this paper presents a novel
AQM scheme supporting TCP flows to avoid congestion. ESO could estimate the plant
dynamics in presence of variation in network parameters from figure: 3.
3) ESO along with PD control helps to compensate the plant of TCP/AQM. From the figure:
5 asymptotic stability is assured for the dynamic system. Tuning of PD control is much
simpler when ESO is introduced.
4) From figure:2 and 4 it can observed that robust control is achieved by just feeding o/p of
the plant along with reference i/p to ESO. So practically even if plant knowledge is not
known, robust control can be achieved as shown in o/p figure: 3, 5 & 6.

poses transfer function as unity, i.e.‫ܩ‬௦ ሺ‫ݏ‬ሻ ൌ 1. But practically sensor causes phase lag,
5) Sensor which is used as a feedback to the controller to control the plant should ideally

attenuation and electromagnetic interference which makes ‫ܩ‬௦ ሺ‫ݏ‬ሻ ് 1 a small change in ‫ܩ‬௦ ሺ‫ݏ‬ሻ
can misguide the controller and corrupt the o/p of the plant and also causes wastage of power.
From figure:4 it can been seen that, sensor o/p is not directly feeded to the controller instead
it has been feeded to ESO and o/p of ESO generated by correcting the deviation between the
model and actual o/p i.e. an observe state is feeded to controller proves to be more superior
than sensor o/p.

ACKNOWLEDGMENT

The authors would like to thank to Prof: VattiRambabuArgunrao from Vishwakarma
Institute of Technology and Prof: Prasheel V. Suryawanshi from MIT Academy of
Engineering for many fruitful discussions.

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AUTHORS’ INFORMATION

KaliprasadA.Mahapatro He received his Bachelors of engineering
in Electronics & Telecommunication from University of PUNE, INDIA in
2010. His basic area of interest is in control system & embedded system
Design, Robotics. He worked as a Junior Research Fellow (JRF) for
Department of Atomic Energy-Board of Research in Nuclear Science. His
research is carried designing a Control Scheme for a class of Non-Linear
System. Currently he currently is pursuing his Master’s degree in Signal
Processing from Vishwakarma Institute of Technology, Pune University

MilindE.Rane. He received his BE degree in Electronics
engineering from University of Pune and M.Tech in Digital Electronics
from Visvesvaraya Technological University, Belgaum, in 1999 and
2001 respectively.His research interest includes image processing,
pattern recognition and Biometrics Recognition

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A novel approach for internet congestion control using an extended state observer 2

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A novel approach for internet congestion control using an extended state observer 2