CN103139090A - Fuzzy discrete global sliding mode congestion control method in Internet - Google Patents

Abstract

The invention relates to a fuzzy discrete global sliding mode congestion control method in the Internet and belongs to the field of internet congestion control. The fuzzy discrete global sliding mode congestion control method aims to solve the problem of congestion in the Internet, combines the time-space (T-S) fuzzy control with the discrete global sliding mode control, and conducts the congestion control over the Internet together. The fuzzy discrete global sliding mode congestion control method comprises the following steps: firstly, by means of selection of a fuzzy rule and a membership function, building a T-S fuzzy model on a non-linear network congestion control system, and representing changes of the network parameter by means of introduction of an uncertain item which is time-varying and time-delay; then, designing an asymptotically-stable discrete global sliding mode surface by means of a layer management interface (LMI) design, and eliminating an approaching process of the system. Moreover, the chattering phenomenon of the system can be effectively reduced by means of a designed controller. The fuzzy discrete global sliding mode congestion control method in the Internet still has good robustness in a wide range of network parameter changes.

Description

Fuzzy discrete global sliding mode jamming control method in the Internet

Technical field

The invention belongs to congestion control field, the Internet.

Background technology

Extensive use along with technology such as gigabit Ethernet, optical networkings, the Internet just progressively enters interconnected stage of high speed of future generation, all trades and professions of China, especially large and medium-sized state-owned enterprise, in order to realize increasing information exchange, the participation of more too busy to get away high speed internet.Yet along with the sharply expansion of internet scale, congestion phenomenon happens occasionally, and for solving congestion problems, in recent years, many jamming control methods in succession occurred.(IEEE Transactions on Automatic Control, 2004,49 (6): 1031-1036), the author is based on H at document On the design of AQM supporting TCP flows using robust control theory _∞Control theory has been carried out the active queue management controller's design to the network congestion control system of time lag, and its performance is better than traditional RED and PI controller.At document A prediction-based active queue management for TCP networks (IEEE Symposium on Computers and Communications, 2012:271-276), the control method α that the author proposes _ SNFAQM can go out congested generation by look-ahead, makes the queue length in router keep stable.

But because the Internet is comprised of the computing terminal, router and the link that are distributed in all over the world various different models, difference in functionality, these equipment vary, uncertain factor is like the shadow following the person, thus the robustness of control method in other words robustness just seem particularly important.And the sliding mode in discrete sliding mode control is only relevant with the concrete form of sliding-mode surface, even contain uncertain factor in system itself, as long as the mathematic(al) representation of sliding-mode surface is determined, the motion of the sliding formwork on sliding-mode surface is just irrelevant with these uncertain factors, have desirable robustness, these characteristics make sliding formwork control the congestion control that is specially adapted to the Internet.In recent years, some sliding formwork jamming control methods have appearred in succession.At document Active queue management (AQM) for TCP/IP networks using discrete time sliding mode control (DSMC) (Proceedings of the 2005 IEEE Conference on Control Applications, Toronto, Canada, 2005:727-730), author designed discrete sliding mode AQM controller, effectively suppressed uncertain and the impact time lag factor, improved to a certain extent the service quality of network.At document Sliding mode based AQM for robust control of IP based network (International Conference on Control, Automation and Systems, Kintex, Korea, 2011:149-154), the author utilizes the theoretical and LMI technology of sliding formwork, to the Design of Network System of non-matching uncertain and time lag the SMC controller, to the time change factor have robustness preferably.At document Discrete-time sliding-mode congestion control in multisource communication networks with time-varying delay (IEEE Transactions on Control Systems Technology, 2011,19 (4): 852-867), the author considered in the network the time become the time lag factor, designed discrete sliding mode AQM controller, reduced the Loss Rate of packet in the available bandwidth scope.

Yet the method in above-mentioned document but mostly exists deficiency separately, if any method propose for continuous time system; Chattering phenomenon in some methods is too obvious; Some methods do not consider uncertain and the impact time lag factor; Some methods propose for the linear network Congestion Control Model, and model accuracy is not high etc.In a word, this field still has certain research space.

Summary of the invention

The object of the invention is to propose a kind of fuzzy discrete global sliding mode jamming control method, in order to solving the congestion phenomenon in the Internet, thereby reduce packet loss, shorten formation time delay end to end, improve the service quality of network.The invention is characterized in that the method contains has the following steps:

(A) initialization W (t), q (t), N (t), C (t), R (t) and p (t) network parameter, initial value is expressed as respectively W ₀, q ₀, N, C, R ₀And p ₀Wherein: W (t) represents the window size of TCP network, q (t) represents queue length current in router, the linking number that N (t) representative activates, C (t) represents the trunk link capacity, R (t) represents round-trip delay, 0≤p (t)≤1 representative grouping abandons/marking probability, W ₀Represent the desired value of TCP network window, q ₀Represent the queue length of expecting in router, N, C and R ₀Be respectively N (t), the nominal value of C (t) and R (t), p ₀=2N ²/ (R ₀ ²C ²);

(B) take 0.002s as the sampling period, the Frame that enters into router is sampled;

(C) if the sampling time does not arrive, wait for, if the sampling time arrives, read W (t), q (t), N (t), C (t), the numerical value of R (t) and p (t);

(D) for suc as formula the nonlinear network congestion control system shown in (1)

$\stackrel{\·}{x}\left(t\right)=F(x,u)=a\left(x\right)+b\left(x\right)u\left(t\right)---\left(1\right)$

Wherein:

$\stackrel{\&CenterDot;}{x}\left(t\right)=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_2\left(t\right)\end{array}\right],$ x ₁(t)=q(t)-q ₀，x ₂(t)=W(t)-W ₀， $a\left(x\right)=\left[\begin{array}{c}{a}_1\left(x\right)\\ a_2\left(x\right)\end{array}\right],$ $b\left(x\right)=\left[\begin{array}{c}{b}_1\left(x\right)\\ b_2\left(x\right)\end{array}\right],$ U (t)=p (t)-p ₀And-p ₀≤ u (t)≤1-p ₀, $a_1\left(x\right)=\frac{N\left(t\right)}{\mathrm{\&tau;}\left(t\right)}[x_2\left(t\right)+W_0]-C\left(t\right),$ $a_2\left(x\right)=\frac{1}{\mathrm{\&tau;}\left(t\right)}-\frac{[x_2\left(t\right)+W_0][x_2(t-\mathrm{\&tau;}\left(t\right))+W_0]}{2\mathrm{\&tau;}\left(t\right)}{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA00002842523400012.png,HDA00002842523400013.png"\; state="\{\{state\}\}">p</figure-callout>}}_0,$ b ₁(x)=0， $b_2\left(x\right)=-\frac{[x_2\left(t\right)+W_0][x_2(t-\mathrm{\&tau;}\left(t\right))+W_0]}{2\mathrm{\&tau;}\left(t\right)},$ τ(t)=R(t)，

By selecting two fuzzy rules to carry out the T-S obscurity model building; Described two fuzzy rules are:

Rule 1: if W (t) is at W ₀Near and q (t) at q ₀Near, so

$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{1}x\left(t\right)+\mathrm{Bu}\left(t\right)---\left(2\right)$

Rule 2: if W (t) is at W ₀Near and q (t) near the largest buffered of congested router, so

$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{2}x\left(t\right)+\mathrm{Bu}\left(t\right)---\left(3\right)$

(E) the discretization processing is carried out in the mathematic(al) representation of two fuzzy rules, and introduce the indeterminate that band becomes time lag sometimes in model, represent N (k) with this, the uncertain factor that the actual change of C (k) and R (k) is brought;

(F) x in the mathematic(al) representation of two fuzzy rules (k) is done linear transformation, make it to become z (k);

(G) by selecting membership function Τ _ij(z _j(k)), thus obtain overall L-R fuzzy number;

(H) utilize LMI to determine the expression of asymptotically stable discrete global sliding mode face S (k);

The concrete network parameter that obtains when (I) utilizing overall L-R fuzzy number in step (G), the discrete global sliding mode face S (k) in step (H), discrete Reaching Law and sampling obtains the concrete numerical value of fuzzy discrete global sliding mode congestion controller u (k);

(J) if in step (I), the concrete numerical value of u (k) is at-p ₀And 1-p ₀Between, this numerical value remains unchanged, if this numerical value is less than-p ₀, u (k)=-p ₀If this numerical value is greater than 1-p ₀, u (k)=1-p ₀

(K) with u (k)+p ₀For probability to the packet that enters into router abandon/mark processes, and returns to response packet with congested cue mark with this probability to transmitting terminal.

The present invention compares with existing method, has following advantage:

(1) strong robustness.Because it is exactly that the sliding formwork motion has consistency that sliding formwork is controlled maximum advantage, consistency is called again desirable robustness, the internet environment that becomes when this specific character more can adapt to.What this method was used is that discrete global sliding mode is controlled, and has eliminated the approach procedure of discrete system, and the whole process that makes system motion is all the discrete sliding mode motion, so strong robustness.

(2) model accuracy is high.The method is based on the nonlinear network Congestion Control Model, on this model basis by selecting fuzzy rule and membership function to carry out the T-S obscurity model building, rather than based on linear network Congestion Control Model design control method, introduced in model simultaneously and be with the indeterminate that sometimes becomes time lag to come the variation of equivalent network parameters.Therefore, the method based on the precision of Mathematical Modeling high.

In a word, the present invention combines T-S fuzzy control and the control of discrete global sliding mode, jointly carries out the congestion control of the Internet.At first by selecting fuzzy rule and membership function, nonlinear network congestion control system is set up the T-S fuzzy model, and represent the variation of network parameter with the indeterminate that sometimes becomes time lag by introducing, then utilize the asymptotically stable discrete global sliding mode face of LMI design, eliminated the approach procedure of system, and designed controller can effectively reduce the chattering phenomenon of system.The present invention still has good robustness in wider network parameter excursion, thereby can guarantee that network has higher bandwidth availability ratio and lower end-to-end time delay.

Description of drawings

Fig. 1 artificial network topology diagram.

The static properties of Fig. 2 network.

The robust performance when linking number that Fig. 3 activates changes.

Robust performance when Fig. 4 trunk link capacity changes.

Robust performance when Fig. 5 round-trip delay changes.

Robust performance when each network parameter of Fig. 6 all changes.

Embodiment

Embodiment 1

Existing document has provided nonlinear the Internet Congestion Control Model, and is as follows:

$\stackrel{\&CenterDot;}{x}\left(t\right)=F(x,u)=a\left(x\right)+b\left(x\right)u\left(t\right)---\left(1\right)$

Wherein:

$\stackrel{\&CenterDot;}{x}\left(t\right)=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_2\left(t\right)\end{array}\right],$ $a\left(x\right)=\left[\begin{array}{c}{a}_1\left(x\right)\\ a_2\left(x\right)\end{array}\right],$ $b\left(x\right)=\left[\begin{array}{c}{b}_1\left(x\right)\\ b_2\left(x\right)\end{array}\right],$ U (t)=p (t)-p ₀And-p ₀≤ u (t)≤1-p ₀, $a_1\left(x\right)=\frac{N\left(t\right)}{\mathrm{\&tau;}\left(t\right)}[x_2\left(t\right)+W_0]-C\left(t\right),$ $a_2\left(x\right)=\frac{1}{\mathrm{\&tau;}\left(t\right)}-\frac{[x_2\left(t\right)+W_0][x_2(t-\mathrm{\&tau;}\left(t\right))+W_0]}{2\mathrm{\&tau;}\left(t\right)}{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA00002842523400012.png,HDA00002842523400013.png"\; state="\{\{state\}\}">p</figure-callout>}}_0,$ b ₁(x)=0， $b_2\left(x\right)=-\frac{[x_2\left(t\right)+W_0][x_2(t-\mathrm{\&tau;}\left(t\right))+W_0]}{2\mathrm{\&tau;}\left(t\right)},$ x ₁(t)=q (t)-q ₀, x ₂(t)=W (t)-W ₀, τ (t)=R (t), q (t) is queue length current in router, q ₀Be the queue length of expecting in router, W (t) is the window size of TCP network, W ₀Be the desired value of TCP network window, the linking number of N (t) for activating, C (t) is the trunk link capacity, and R (t) is round-trip delay, and 0≤p (t)≤1 abandons/marking probability for grouping, p ₀=2N ²/ (R ₀ ²C ²), N, C and R ₀Be respectively N (t), the nominal value of C (t) and R (t) (concrete numerical value should carry out the long-term result that obtains of monitoring to network according to network monitoring department in the past to be decided).

Formula (1) is carried out the modeling of T-S fuzzy model, selects two following fuzzy rules:

Rule 1: if W (t) is at W ₀Near and q (t) at q ₀Near, so

$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{1}x\left(t\right)+\mathrm{Bu}\left(t\right)---\left(2\right)$

Rule 2: if W (t) is at W ₀Near and q (t) near the largest buffered of congested router, so

$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{2}x\left(t\right)+\mathrm{Bu}\left(t\right)---\left(3\right)$

Wherein: A ₁, A ₂To obtain according to the method in existing document with the value of B, namely

$A_1=\frac{\&PartialD;F}{\&PartialD;x}{|}_{\begin{array}{c}x\left(t\right)=0\\ u\left(t\right)=0\end{array}},$ ${A_2}^T=\left[\begin{array}{cc}\&dtri;a_1\left(\mathrm{\&theta;}\right)+\frac{a_1\left(\mathrm{\&theta;}\right)-{x_0}^T\&dtri;a_1\left(\mathrm{\&theta;}\right)}{{{\left|\right|\mathrm{\&theta;}\left|\right|}_2}^2}\mathrm{\&theta;}& \&dtri;a_2\left(\mathrm{\&theta;}\right)+\frac{a_2\left(\mathrm{\&theta;}\right)-{x_0}^T\&dtri;a_2\left(\mathrm{\&theta;}\right)}{{{\left|\right|\mathrm{\&theta;}\left|\right|}_2}^2}\mathrm{\&theta;}\end{array}\right],$ $B=\frac{\&PartialD;F}{\&PartialD;u}{|}_{\begin{array}{c}x\left(t\right)=0\\ u\left(t\right)=0\end{array}},$ ▽ is gradient, and θ is that W (t) is at W ₀Near and q (t) congested router largest buffered vicinity a bit.

Formula (2) and formula (3) are carried out the discretization processing, and the introducing indeterminate represents N (k), the uncertain factor that the actual change of C (k) and R (k) is brought (N (k), C (k), R (k) is respectively N (t), C (t), the corresponding centrifugal pump of R (t)), formula (2) and formula (3) turn to

x(k+1)=G _ix(k)+Hu(k)+μ _1iF _i(k)x(k)+μ _2iF _di(k)x(k-τ(k)) (i=1,2) (4)

Wherein: $G_i=e^{A_{i}T},$ $H=\left[\begin{array}{c}{h}_1\\ h_2\end{array}\right]=\left({\&Integral;}_0^T{e}^{A_{1}t}\mathrm{dt}\right)\&times;B,$ ${\mathrm{\&mu;}}_{1i}=\underset{\begin{array}{c}N1\&le;N\left(k\right)\&le;N2\\ C1\&le;C\left(k\right)\&le;C2\\ R1\&le;R\left(k\right)\&le;R2\end{array}}{\max }\left|\right|\left|G_i\left(k\right)\right||-|\left|G\right|\left|\right|,$ μ _2i=0.25 μ _1i, T=0.002s is the sampling period ,-p ₀≤ u (k)≤1-p ₀, G _i(k) the same G of computing formula _iJust it is according to the N (k) that changes, C (k) and R (k) obtain, N1 and N2 are the bounds that N (k) changes, C1 and C2 are the bounds that C (k) changes, R1 and R2 are the bounds (the concrete numerical value of these bounds should carry out the long-term result that obtains of monitoring to network according to network monitoring department in the past to be decided) that R (k) changes, F _i(k) and F _di(k) be indeterminate, and satisfy respectively F _i ^T(k) F _i(k)≤I, $F_{\mathrm{di}}^T\left(k\right)F_{\mathrm{di}}\left(k\right)\&le;I.$

X (k) in formula (4) is done following linear transformation:

$z\left(k\right)=\left[\begin{array}{c}{z}_1\left(k\right)\\ z_2\left(k\right)\end{array}\right]=\left[\begin{array}{c}{x}_1\left(k\right)-x_2\left(k\right)h_1/h_2\\ x_2\left(k\right)/h_2\end{array}\right]---\left(5\right)$

Formula (4) can turn to following form:

$z(k+1)={\stackrel{\&OverBar;}{G}}_{i}z\left(k\right)+{\mathrm{\&mu;}}_{1i}{\stackrel{\&OverBar;}{F}}_i\left(k\right)z\left(k\right)+{\mathrm{\&mu;}}_{2i}{\stackrel{\&OverBar;}{F}}_{\mathrm{di}}\left(k\right)z(k-\mathrm{\&tau;}\left(k\right))+\stackrel{\&OverBar;}{H}u\left(k\right)(i=\mathrm{1,2})---\left(6\right)$

Select membership function Τ _ij(z _j(k)) (i=1,2, j=1,2) here is following form:

Τ ₁₁(z ₁(k))=arctg(-z ₁ ²)+π/2，Τ ₁₂(z ₂(k))=arctg(-z ₂ ²)+π/2，Τ ₂₁(z ₁(k))=arctg(-z ₁ ²)+π/2， $T_{22}\left(z_2\left(k\right)\right)=\left\{\begin{array}{cc}\mathrm{arctg}(-{(z_2-\mathrm{\&theta;}/h_2)}^2)+\mathrm{\&pi;}/2,& (z_2\left(k\right)<\mathrm{\&theta;}/h_2)\\ 0,& (z_2\left(k\right)\&GreaterEqual;\mathrm{\&theta;}/h_2)\end{array}\right...$

Can obtain the following overall L-R fuzzy number corresponding with formula (6):

$z(k+1)=\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{\&Theta;}}_i\left(z\left(k\right)\right)\{{\stackrel{\&OverBar;}{G}}_{i}z\left(k\right)+{\mathrm{\&mu;}}_{1i}{\stackrel{\&OverBar;}{F}}_i\left(k\right)z\left(k\right)+{\mathrm{\&mu;}}_{2i}{\stackrel{\&OverBar;}{F}}_{\mathrm{di}}\left(k\right)z(k-\mathrm{\&tau;}\left(k\right))+\stackrel{\&OverBar;}{H}u\left(k\right)\}---\left(7\right)$

Wherein: ${\mathrm{\&Theta;}}_i\left(z\left(k\right)\right)=\frac{{\mathrm{\&Lambda;}}_i\left(z\left(k\right)\right)}{\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{\&Lambda;}}_i\left(z\left(k\right)\right)},$ ${\mathrm{\&Lambda;}}_i\left(z\left(k\right)\right)=\underset{j=1}{\overset{2}{\mathrm{\&Pi;}}}{T}_{\mathrm{ij}}\left(z_j\left(k\right)\right).$

Order ${\mathrm{\&mu;}}_{1i}{\stackrel{\&OverBar;}{F}}_{i11}\left(k\right)=F\left(k\right){\mathrm{\&Omega;}}_{i1,}$ ${\mathrm{\&mu;}}_{1i}{\stackrel{\&OverBar;}{F}}_{i12}\left(k\right)=F\left(k\right){\mathrm{\&Omega;}}_{i2},$ ${\mathrm{\&mu;}}_{2i}{\stackrel{\&OverBar;}{F}}_{\mathrm{di}11}\left(k\right)=F\left(k\right){\mathrm{\&Omega;}}_{i3},$ ${\mathrm{\&mu;}}_{2i}{\stackrel{\&OverBar;}{F}}_{\mathrm{di}12}\left(k\right)=F\left(k\right){\mathrm{\&Omega;}}_{i4},$ F (k) bending moment battle array and satisfy F when uncertain ^T(k) F (k)≤I,

With

Be matrix

The element of middle relevant position,

With Be matrix

The element of middle relevant position, Ω _i1, Ω _i2, Ω _i3And Ω _i4Constant matrices for corresponding dimension.

Discrete global sliding mode face S (k) is chosen to be

S(k)=Lz(k)-Lz(0)=-lz ₁(k)+z ₂(k)+Ψ ₁l-Ψ ₂ (8)

Wherein: L=[-l 1], Ψ ₁=z ₁(0), Ψ ₂=z ₂(0), for making the sliding formwork motion Asymptotic Stability on this sliding-mode surface, l is determined by following LMI:

Wherein: i=1,2,

Ξ ₂=-Ψ ₁(Ω _i2+ Ω _i4) W+ Ψ ₂(Ω _i2+ Ω _i4) X, W=lX,

λ〉0 be constant.

Discrete Reaching Law S (k+1)=(1-qT) S (k) in the existing document of utilization-ε T (1-e ^{-‖ z (k) ‖}) signS (k) (making q=20 here, ε=5) and formula (7) and formula (8) can get fuzzy discrete global sliding mode congestion controller u (k) and be

$u\left(k\right)=-{\left(L\stackrel{\&OverBar;}{H}\right)}^{-1}\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{\&Theta;}}_i\left(z\left(k\right)\right)\{L{\stackrel{\&OverBar;}{G}}_{i}z\left(k\right)+L{\stackrel{\&OverBar;}{f}}_i(k-1)-\mathrm{Lz}\left(k\right)+20\mathrm{TS}\left(k\right)+5T(1-e^{-\left|\right|z\left(k\right)\left|\right|})\mathrm{signS}\left(k\right)\}---\left(10\right)$

Wherein: ${\stackrel{\&OverBar;}{f}}_i(k-1)=z\left(k\right)-{\stackrel{\&OverBar;}{G}}_{i}z(k-1)+\stackrel{\&OverBar;}{H}u(k-1).$

Can obtain the concrete numerical value of u (k) according to formula (10) and the network parameter that obtains of sampling, if this numerical value is at-p ₀And 1-p ₀Between, this numerical value remains unchanged, if this numerical value is less than-p ₀, u (k)=-p ₀If this numerical value is greater than 1-p ₀, u (k)=1-p ₀Because this controller makes system when the stable state, its running orbit and the same 5T||z of the distance of discrete global sliding mode face (k) || be directly proportional, and 5T||z (k) during stable state || numerical value very little, therefore, chattering phenomenon during stable state is very little, is reflected in congestion control the i.e. effectively steady oscillation of inhibitory control target (being the queue length in router) of this controller.

We suppose that the nominal value of N (t) is 300, and between 200 to 400 change at random; The nominal value of C (t) is 2 * 10 ⁴Packets/s ((1packet is 1000bit, i.e. C=20Mbps), and between 12Mbps to 28Mbps change at random; The nominal value of R (t) is 130ms, and between 80ms to 180ms change at random.The maximum of tcp window is taken as 15packets, the desired value of tcp window is taken as 8packets, and the initial value of tcp window is taken as 4packets, and the largest buffered of router is 600packets, the queue length of expectation is taken as 350packets, and initial queue length is taken as 55packets.

Get p by above-mentioned network parameter ₀=2.6627 * 10 ^-8, get according to formula (2) and formula (3) $A_1=\left[\begin{array}{cc}0& 2.3077\&times;{10}^3\\ 0& -8.8757\&times;{10}^{-4}\end{array}\right],$ $A_2=\left[\begin{array}{cc}80& 2.3077\&times;{10}^3\\ -9.2308\&times;{10}^{-5}& 1.7751\&times;{10}^{-3}\end{array}\right],$ $B=\left[\begin{array}{c}0\\ -2.8888\&times;{10}^8\end{array}\right],$ θ=(2.5 * 10 ⁵, 0), get according to formula (4) $G_1=\left[\begin{array}{cc}1& 4.6154\\ 0& 0.9999\end{array}\right],$ $G_2=\left[\begin{array}{cc}1.1735& 5.0051\\ -2.0021\&times;{10}^{-7}& 1.0001\end{array}\right],$ $H=\left[\begin{array}{c}-1.3333\&times;{10}^6\\ -5.7777\&times;{10}^5\end{array}\right],$ μ ₁₁=5.3845, μ ₁₂=6.2035, μ ₂₁=1.3461, μ ₂₂=1.5509, get according to formula (5) and formula (6) ${\stackrel{\&OverBar;}{G}}_1=\begin{array}{c}\left[\begin{array}{cc}1& -2.6666\&times;{10}^6\\ 0& 0.9999\end{array}\right],\end{array}$ ${\stackrel{\&OverBar;}{G}}_2=\left[\begin{array}{cc}1.1735& 5.0051\\ -2.0021\&times;{10}^{-7}& 1.0001\end{array}\right],$ $\stackrel{\&OverBar;}{H}=\left[\begin{array}{c}0\\ 1\end{array}\right],$ Get $F_i\left(k\right)=\left[\begin{array}{cc}{\mathrm{\&alpha;}}_i& 0\\ 0& {\mathrm{\&beta;}}_i\end{array}\right],$ $F_{\mathrm{di}}\left(k\right)=\left[\begin{array}{cc}{\mathrm{\&alpha;}}_{\mathrm{di}}& 0\\ 0& {\mathrm{\&beta;}}_{\mathrm{di}}\end{array}\right],$ α _i, β _i, α _diAnd β _diBe the random number between 0 to 1.Get L=[1.5027 1 according to formula (8) and formula (9)], in above-mentioned parameter substitution formula (10), can get the definite mathematic(al) representation of controller u (k), namely obtained fuzzy discrete global sliding mode jamming control method.In order to narrate conveniently, with the method called after FDGSMC method.

FDGSMC method of the present invention may be summarized to be following steps:

(A) initialization W (t), q (t), N (t), C (t), R (t) and p (t) network parameter, initial value is expressed as respectively W ₀, q ₀, N, C, R ₀And p ₀Wherein: W (t) represents the window size of TCP network, q (t) represents queue length current in router, the linking number that N (t) representative activates, C (t) represents the trunk link capacity, R (t) represents round-trip delay, 0≤p (t)≤1 representative grouping abandons/marking probability, W ₀Represent the desired value of TCP network window, q ₀Represent the queue length of expecting in router, N, C and R ₀Be respectively N (t), the nominal value of C (t) and R (t), p ₀=2N ²/ (R ₀ ²C ²);

(B) take 0.002s as the sampling period, the Frame that enters into router is sampled;

(C) if the sampling time does not arrive, wait for, if the sampling time arrives, read W (t), q (t), N (t), C (t), the numerical value of R (t) and p (t);

(D) for carrying out the T-S obscurity model building suc as formula the nonlinear network congestion control system shown in (1), set up suc as formula two fuzzy rules shown in (2) and formula (3);

(E) formula (2) and formula (3) are carried out the discretization processing, and introduce in model and be with the indeterminate that sometimes becomes time lag, represent N (k) with this, the uncertain factor that the actual change of C (k) and R (k) is brought, formula (2) and formula (3) can be expressed as formula (4);

(F) x (k) in formula (4) is done suc as formula the linear transformation shown in (5), formula (4) can turn to the form of formula (6);

(G) select membership function Τ _ij(z _j(k)), obtain overall L-R fuzzy number formula (7) corresponding to formula (6);

(H) utilize formula (8) and formula (9) to determine the expression of asymptotically stable discrete global sliding mode face S (k);

The concrete network parameter that obtains when (I) utilizing formula (7), formula (8), discrete Reaching Law and sampling obtains the concrete numerical value of fuzzy discrete global sliding mode congestion controller u (k);

(J) if the concrete numerical value of the u (k) in step (I) at-p ₀And 1-p ₀Between, this numerical value remains unchanged, if this numerical value is less than-p ₀, u (k)=-p ₀If this numerical value is greater than 1-p ₀, u (k)=1-p ₀

(K) with u (k)+p ₀For probability to the packet that enters into router abandon/mark processes, and returns to response packet with congested cue mark with this probability to transmitting terminal.

We utilize the NS2 Network Simulation Software to carry out emulation to the FDGSMC method.The topological structure of artificial network as shown in Figure 1, packet sends between side a and b, router-A is congested node, our FDGSMC method is operated in wherein.At first, tested the static properties of the method, i.e. the selection of network parameter as previously mentioned, suppose that just N (t) is that 300, C (t) is 20Mbps, R (t) is 130ms, namely be nominal value separately, and do not change, simulation result as shown in Figure 2.As can be seen from Figure 2: the FDGSMC method makes our control target, and namely very rapid convergence is near desired value for the queue length in router, and the overshoot of whole process is very little, and during stable state, queue length has reached desired value basically.Due in the Internet of reality, network parameter is often to change, therefore, the FDGSMC method is very important to the quality of the robust performance that the network parameter that changes has, for this reason, next we are the linking number N (t) that activates, trunk link capacity C (t) and round-trip delay R (t) respectively between 200 to 400, change at random between 12Mbps to 28Mbps, between 80ms to 180ms, simulation result is respectively as Fig. 3, Fig. 4 and shown in Figure 5.Can find out from Fig. 3 to Fig. 5: in the incipient stage, queue length in router has some vibrations, but after the shorter adjustment time, queue length is very fast just can be converged near desired value, can satisfy the requirement of the discrete Reaching Law of effective reduction buffeting due to the FDGSMC method, therefore, the steady oscillation of queue length is all smaller.At last, in the situation that the equal change at random in above-mentioned excursion of each network parameter has been carried out l-G simulation test, result as shown in Figure 6.As can be seen from Figure 6: in the situation that each network parameter all changes, the FDGSMC method still can make the queue length in router converge near desired value, just because uncertain factor is larger, so adjustment time and steady oscillation slightly increase.In a word, the static properties of FDGSMC method and robust performance are all very good, the internet environment that becomes in the time of can adapting to, thus can effectively suppress congestion phenomenon.

Claims (1)

1. the fuzzy discrete global sliding mode jamming control method in a Internet, is characterized in that comprising the steps:

(A) initialization W (t), q (t), N (t), C (t), R (t) and p (t) network parameter, initial value is expressed as respectively W ₀, q ₀, N, C, R ₀And p ₀Wherein: W (t) represents the window size of TCP network, q (t) represents queue length current in router, the linking number that N (t) representative activates, C (t) represents the trunk link capacity, R (t) represents round-trip delay, 0≤p (t)≤1 representative grouping abandons/marking probability, W ₀Represent the desired value of TCP network window, q ₀Represent the queue length of expecting in router, N, C and R ₀Be respectively N (t), the nominal value of C (t) and R (t), p ₀=2N ²/ (R ₀ ²C ²);

(B) take 0.002s as the sampling period, the Frame that enters into router is sampled;

(C) if the sampling time does not arrive, wait for, if the sampling time arrives, read W (t), q (t), N (t), C (t), the numerical value of R (t) and p (t);

(D) for suc as formula the nonlinear network congestion control system shown in (1)

$\stackrel{\&CenterDot;}{x}\left(t\right)=F(x,u)=a\left(x\right)+b\left(x\right)u\left(t\right)---\left(1\right)$

Wherein:

$\stackrel{\&CenterDot;}{x}\left(t\right)=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_2\left(t\right)\end{array}\right],$ x ₁(t)=q(t)-q ₀，x ₂(t)=W(t)-W ₀， $a\left(x\right)=\left[\begin{array}{c}{a}_1\left(x\right)\\ a_2\left(x\right)\end{array}\right],$ $b\left(x\right)=\left[\begin{array}{c}{b}_1\left(x\right)\\ b_2\left(x\right)\end{array}\right],$ U (t)=p (t)-p ₀And-p ₀≤ u (t)≤1-p ₀, $a_1\left(x\right)=\frac{N\left(t\right)}{\mathrm{\&tau;}\left(t\right)}[x_2\left(t\right)+W_0]-C\left(t\right),$ $a_2\left(x\right)=\frac{1}{\mathrm{\&tau;}\left(t\right)}-\frac{[x_2\left(t\right)+W_0][x_2(t-\mathrm{\&tau;}\left(t\right))+W_0]}{2\mathrm{\&tau;}\left(t\right)}{p}_0,$ b ₁(x)=0， $b_2\left(x\right)=\frac{[x_2\left(t\right)+W_0][x_2(t-\mathrm{\&tau;}\left(t\right))+W_0]}{2\mathrm{\&tau;}\left(t\right)},$ τ(t)=R(t)，

By selecting two fuzzy rules to carry out the T-S obscurity model building; Described two fuzzy rules are:

Rule 1: if W (t) is at W ₀Near and q (t) at q ₀Near, so

$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{1}x\left(t\right)+\mathrm{Bu}\left(t\right)---\left(2\right)$

Rule 2: if W (t) is at W ₀Near and q (t) near the largest buffered of congested router, so

$\stackrel{\&CenterDot;}{x}\left(t\right)=A_{2}x\left(t\right)+\mathrm{Bu}\left(t\right)---\left(3\right)$

(E) the discretization processing is carried out in the mathematic(al) representation of two fuzzy rules, and introduce the indeterminate that band becomes time lag sometimes in model, represent N (k) with this, the uncertain factor that the actual change of C (k) and R (k) is brought;

(F) x in the mathematic(al) representation of two fuzzy rules (k) is done linear transformation, make it to become z (k);

(G) by selecting membership function Τ _ij(z _j(k)), thus obtain overall L-R fuzzy number;

(H) utilize LMI to determine the expression of asymptotically stable discrete global sliding mode face S (k);

The concrete network parameter that obtains when (I) utilizing overall L-R fuzzy number in step (G), the discrete global sliding mode face S (k) in step (H), discrete Reaching Law and sampling obtains the concrete numerical value of fuzzy discrete global sliding mode congestion controller u (k);

(J) if in step (I), the concrete numerical value of u (k) is at-p ₀And 1-p ₀Between, this numerical value remains unchanged, if this numerical value is less than-p ₀, u (k)=-p ₀If this numerical value is greater than 1-p ₀, u (k)=1-p ₀

(K) with u (k)+p ₀For probability to the packet that enters into router abandon/mark processes, and returns to response packet with congested cue mark with this probability to transmitting terminal.

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