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

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN

0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME

80

A NOVEL APPROACH FOR INTERNET CONGESTION CONTROL

USING AN EXTENDED STATE OBSERVER

Kaliprasad A. Mahapatro1, MilindE.Rane

2

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

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81

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

�� (1)

�� , �� 0��0, �� 0 (2)

whereW& q is the maximum window size and average queue length(i.e. buffer size), they

are the positive bounded quantities i.e.,� ! "0,�# $ and � ! "0, �%$. The congestion of window

size is increased after every round-trip time R(t). p(.) denotes the (input function) packet drop

probability p(t) &[0, 1] and output is queue velocity��_ To linearize equation(1) following

assumptions are made[4]

• active TCP session N(t) are time invariant

i.e. N (t) & N.

• transmission link capacity are time invariant

i.e. C (t) &C.

• time delay argument � � �on queue length q is assumed to be fixed to � � �'then

the linearize model of equation(1) results into

(�� )*+� �(�� (�� '�� )*+ �(�� (�� '�� )*+��* (�� '� (3)

(�� ) (�� ) (�� (4)

where W(t) and _q(t)are the incremental variables w.r.t operating point as a function of

f(�',�', �', �') with a desired equilibrium queue length q0 is given by



83

,-.-/ �' � 0)+ � 12�' � �)+��' � �)*�' � ��345� �6565 75849�

(5)

This lead to a nominal model, and is given as

Fig. 1. Linearized model of TCP/AQM networks

:�;� � <=2�;�<0>?>?�;�5 �)@ (6)

where:�;� is the transfer function of the plant of TCP/AQM network which includes second-

order system and time delay element as shown in Figure: 1

Where <=2�;� and <0>?>?�;� are given as

<=2�;� � ABC**DB*@E *DBAB*C (7)

<0>?>?�;� � DBAB@E FAB (8)

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

:�;� � <'�;�5 �)@ � C**DG@E *DA)*CH�@E FA)� 5 �)@ (9)

In order to illustrate the effectiveness of ESO method, a numerical situation will be presented

by taking network parameter of [4] as C = 3750packets/sec, �' = 175packets, 12 = 0:2sec.

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

:�;� � �.�K�LKMN�'O�@E'.MP��@EQ.�� 5 '.�QR (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 ż1 =

.ξ+ c1 x& (13)

ż1 =.ξ + c1 (Ax +Bu +Bd) ……. from eqn8 (14)

Choosing .ξ as - c1 (Ax+Bu) - c1Bd and sub in 10 we get.......

ż1 = − 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

ż1 = C1 η ................ where C1 = c1B (17)

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

S� � �T� � �� S (18)

or S� � �� S � 0 �19�

Thus by the property of linear differential equation If C1>0 thenS →0. Thus error→0 as we increases

C1 ≫ 0 or C1→∞

This is well explained in Figure: 7.

B. Limitation of Disturbance Observer

The problem with this observer is that it fails when the assumption of X�= 0 is violated. Thus, under

the assumption that X� Y 0 we can write, S� � X� � T�� (20)

= X� � �� η (21)

Or S� � �� S � X� (22)

Thus by the property of linear differential equation ifC1 >0 then S →X� , which state that error

dynamics never reduces to zero under conditionX� Y 0 which is rather a practical case.



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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 = �Z, Z� , [�+ 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

1 2

2 3 0

3

1

x x

x x b u

x h

y x

= = +

= =

&

&

&

(24)

Here \�Z, Z� , [� and its derivative h� \��Z, Z� , [�are assumed to be unknown, it is now possible to

estimate \�Z, Z� , [�by using state estimator for equation 20. HAN proposed a non-linear observer.

1 2 1 1

2 3 2 2 0

3 3 3

( )

( )

( )

z z g e

z z g e b u

z g e

β

β

β

= + = + +

=

&

&

&

(25)

where e=y-T�TP is the estimate of the uncertain function f (.). 4� (.)is modified exponential function given as......

1-

( ) ,( , , )

,

i

i

a

i ia

e sign e eg e a e e

δδ

δδ

= <

>

(26)

Where.......

• ] is chosen between 0 & 1

• 4�is the gain.

• (is the small number used to limit the gain.

• ^ is the observer gain



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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

� � _� � `6� as

a��b � c 0 1�2.173 �4.63i c��i � c 0133.91 N 10Pi 6 (27)

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

Plantj �� k. lmnol � p. qnok � 133.91 N 10P��P � 9Z � �� (28)

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



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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

plant and to ESO s as a reference input.

The difference of output of the plant �� and T�� which is derived ultimately from TP� as

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 ]

Scale ]uis chosen in between 0& 1, because it yields 4u high gain [14] [6]. In our case

we consider for Equation: 26 as.........

- ]� = 1.00

-]� = 0.750

-]P = 0.625

Calculation of ^ Gain bi is adjusted by using pole-placement method. In our case by

using matlab simulation by using place (A’ B’ p) command. ufor Equation: 25

as.........

- � = 109

- ^� = 3858

- ^P = 44640

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

it is taken as for Equation: 26 as.........

- ( = 10 P

Considering values in above subsection and substituting the same in Equation: 28,

25& 26 estimation is carried out in matlab for step in Figure: 3, its seen that TP (Z in

Fig) converges to unknown functionf (.).

V. ROBUST CONTROL

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

closed-loop feedback setting, such as that shown in Figure: 4 for NESO. The profile

generator provides the desired state trajectory in both y and Z� , in simulation we have

used step and sine profile. Based on



88

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

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

assuming that all states are accessible in the control law. In the case of NESO, the extended

state information, TP, which converges to �P � \�Z, Z, [� �is used to compensate for the

unknown \�Z, Z, [� �. In particular, the control law is given as

6 � vwEx?y) (29)

where e = "z� � T� , z� � T�${ and K is the state feedback gain that is equivalent to a

proportional derivative (PD) controller design, and z� � ��| and z� � ��|where ��|is a plant

i/p as shown in figure:4 Substituting (29) in (23)

Z} � �\�Z, Z, [� � � TP� � ~5 (30)

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

a��b � c�10�05i (31)



89

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.



90

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



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VI. CONCLUSION

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

thestate of the plant. As seen from equation: 22 DO fail to estimate the disturbances when

disturbance is not constant i.e. X� Y 0. Therefore Disturbance Observer works fails to

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.

5) Sensor which is used as a feedback to the controller to control the plant should ideally

poses transfer function as unity, i.e.:@�;� � 1. But practically sensor causes phase lag,

attenuation and electromagnetic interference which makes :@�;� Y 1 a small change in :@�;� 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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