; 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

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									   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
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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

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)



                                                                                           (2)



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




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                                                                                           (5)




This lead to a nominal model, and is given as




                       Fig. 1. Linearized model of TCP/AQM networks


                                                                                          (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           and            are given as


                                                                                          (7)



                                                                                          (8)


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


                                                                                          (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, = 0:2sec.
For load of N = 60 TCP sessions, = 0:008& substituting the same in equation (5) we get
    = 15packets, & = 0:246.

                                                                                         (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,

                                                                                               (18)
or



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

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 = 0 is violated. Thus, under
the assumption that       we can write,

                                                                                              (20)

  =              η                                                                            (21)
Or
                                                                                              (22)

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

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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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=              + 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                 and its derivative h              are assumed to be unknown, it is now possible to
estimate
            by using state estimator for equation 20. HAN proposed a non-linear observer.

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

Where.......
       •          is chosen between 0 & 1
       •          is the gain.
       •         is the small number used to limit the gain.
       •          is the observer gain

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

             as

                                                                                               (27)

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




  Plant                                                                                        (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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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

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 which is derived ultimately from 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
Calculation of
Scale is chosen in between 0& 1, because it yields             high gain [14] [6]. In our case
we consider for Equation: 26 as.........
-   = 1.00
-   = 0.750
-   = 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. for Equation: 25
as.........
- = 109
- = 3858
- = 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.........
- =
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   (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 , in simulation we have
used step and sine profile. Based on




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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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            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, , which converges to                          is used to compensate for the
unknown             . In particular, the control law is given as

                                                                                         (29)

where e =                         and K is the state feedback gain that is equivalent to a
proportional derivative (PD) controller design, and        and          where    is a plant
i/p as shown in figure:4 Substituting (29) in (23)

                                                                                          (30)

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

                                                                                          (31)




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




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       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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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
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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.         . 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.            . But practically sensor causes phase lag,
attenuation and electromagnetic interference which makes               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.

REFERENCES

[1] B. Chellaprabha and S. C. Pandian, “A multipath energy efficient congestion control
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[2] D. T. C. V. Hollot, Vishal Misra and W. Gong, “Analysis and design of controllers for
aqm routers supporting tcp flows,” IEEE Transaction on Automatic Control, vol. 47.
[3] G. P. Liansheng Tan, Wei Zhang and G. Chen, “Stability of tcp/red systems in aqm
routers,” IEEE Transaction on Automatic Control, vol. 51.
[4] V. M. A. R. Vilanova, “Robust 2-dof pid control for congestion control of tcp/ip
networks,” Int. J. of Computers, Communications & Control, vol. V, no. 5, pp. 968 – 975,
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[5] S. Mascolo, “Modeling the internet congestion control using a smith controller with input
shaping,” IFAC 03 Workshop on Time -delay Systems, p. CR 2179, 2003.
[6] M. N. Hossein ASHTIANI, HamedMoradi POUR, “Active queue management in tcp
networks based on fuzzy-pid controller,” Applied Computer Science & Mathematics, vol. 6,
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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

[7] T. Alvarez, “Design of pid controllers for tcp/aqm wireless networks,” Proceedings of the
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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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