CN103686776B - Method for controlling stability of delay-related MANETs - Google Patents

Abstract

The invention discloses a method for controlling the stability of delay-related MANETs. The method includes the steps of (1) building a capacity analysis non-cooperative planning game model of the MANETs, (2) equivalently converting the model into a describer, (3) determining the conditions of the asymptotic stability of the describer in the step (2), (4) determining parameters for enabling the conditions in the step (3) to be satisfied, and (5) according to the parameters calculated and obtained in the step (4), adjusting the sensitive degree alphai of a node i in the MANETs to the sending flow speed xi and the sensitive degree betai of the node i to queuing delay with the sending flow speed xi, and achieving control over the capacity stability of the MANETs. The method has the universality on the MANETs with non-competitive conflict-free class MAC protocols, can be achieved only by adjusting the physical properties, such as the adoptive power, the available memory, a signal modulation method and a coding mode, of the node of the MANETs, and is small in calculated amount.

Description

Method for controlling stability of time delay related mobile self-organizing network

Technical Field

The invention relates to a method for controlling the stability of a time delay related mobile self-organizing network.

Background

The network capacity is a Mobile Ad-hoc network (MANETs, MANET is a short term for Mobile Ad hoc network, the Ad hoc network is a self-organizing network and is divided into two types of fixed nodes and Mobile nodes, the MANET refers to the key characteristic that the nodes have the Mobile Ad hoc network, but when the nodes in the MANETs transmit data, a shared channel inevitably has competition, so for a multi-hop service flow, the competition among the flows and the competition in the flows generally exist, partial information flow loss is easily caused, the limited bandwidth resources of the MANETs are unnecessarily wasted, and the network capacity is further reduced. To maximize the utilization of MANETs resources, it is natural to balance the information flow rate across the link, preferably close to the link capacity, rather than constantly oscillating between the remaining bandwidth and full overload, to stabilize MANETs capacity. However, MANETs are distributed time-varying dynamic systems, and the capacity of MANETs is affected by many factors, such as power, bandwidth, communication mode, routing policy, interference model, etc., so that the problem of capacity stability of MANETs becomes a very challenging subject.

Although there are many research results on communication system channel capacity, MANETs capacity, network with base stations and stability of distributed network without central base stations, the MANETs capacity model of the distributed network is mostly a nonlinear dynamic equation, and documents for researching the stability of the nonlinear dynamic equation are not much, so that the MANETs capacity stability analysis is rarely researched.

The MANETs capacity analysis model considering data propagation delay is undoubtedly a nonlinear time-varying system which is widely applied to the fields of aerospace, communication, biological systems and the like, and the existing research on the stability of the MANETs capacity analysis model is poor in practicability because either additional dynamics discussion is introduced during model transformation or a conclusion becomes conservative based on a time-delay independent condition.

The capacity stability research of MANETs under the condition of time-varying propagation delay is still in the initial sprouting stage by utilizing the Lyapunov index stability theory (the Lyapunov index is an important quantitative index for measuring the dynamic characteristics of the system, and the method represents the average index rate of convergence or divergence between adjacent tracks of the system in a phase space, and can be intuitively judged whether the maximum Lyapunov index is greater than zero or not for the existence of dynamic chaos of the system), and particularly, the method is applied to the field of the capacity stability research of the MANETs based on the time-varying propagation delay related nonlinear dynamic differential equation modeling by combining the descriptor technology with a Linear matrix inequality (LMI-Linear matrix inequality) method.

Disclosure of Invention

In view of the above problems in the prior art, the present invention aims to: a method for controlling the stability of a mobile ad hoc network related to time delay is provided.

In order to achieve the purpose, the invention adopts the following technical scheme: a method for controlling the stability of a time delay related mobile self-organizing network comprises the following specific steps:

step 1: establishing a MANETs capacity analysis non-cooperative planning game model as shown in a formula (9),

i=1,2,...,k,m=1,2,...,j,h=1,2,...,k；

step 2: the MANETs capacity analysis non-cooperative planning game model in the step1 is analyzed, the expression (9) is equivalent to the descriptor expression (10),

wherein, C represents constant and can be obtained from actual network performance, x (t) represents the sending flow rate vector of the source node of the mobile self-organizing network, x (t-r (t)) represents the sending flow rate vector of the source node of the mobile self-organizing network added with the propagation delay item, and

f(x(t))=[f₁(x(t))f₂(x(t))...f_i(x(t))...f_k(x(t))]^Tk, k < n, n being the number of nodes of the ad-hoc network, wherein,

g(x(t-r(t)))=[g₁(x(t-r(t)))g₂(x(t-r(t)))...g_i(x(t-r(t)))...g_k(x(t-r(t)))]^Ti =1,2,. k, wherein,

a and B are diagonal matrixes, and specifically are as follows:

representing a source node of the mobile ad hoc network sending a traffic rate change rate vector,h =1, 2.. k denotes a transit linkThe ith flow rate of (c) is,h =1, 2.. k denotes the traffic rate x sent by the source node i_iOver a linkThe number h of (a) is,representing a transit linkThe sum of the flow rates of (a) and (b),(t) represents the time at which the link is traversedThe sum of the flow rates of (a) and (b),(t-r (t)) represents the time delay at time t passing through the linkSum of flow rates of α_iRepresenting node pair sending traffic rate x_iDegree of sensitivity of β_iIndicating that node i employs the sending traffic rate x_iThe degree of sensitivity to the queuing delay,indicating assignment to a linkThe ratio of the time of (a) to (b),represents a link l_iT represents the network running time, r (t) represents the node i sending traffic rate x_iIs passed through the linkm =1, 2.. times, j produces a time-varying propagation delay, s_{m}Representing a feasible link set of a concurrency scene, wherein K represents the number of source nodes, j is the number of links of the mobile ad hoc network, and K represents the source node set;

and step 3: the conditions for gradually stabilizing the descriptors of the MANETs capacity analysis non-cooperative planning game model established in the step2 comprise a condition (13) and a condition (14),

whereinTheta is not less than 0 andθ is a given constant;

wherein,Ω₁₂=P₁-P₂ ^T+C^TP₃，

Ω₂₂=-P₃-P₃ ^T+r R；P₁=P₁ ^T>0,Q=Q^T>0, is a positive definite real symmetric matrix, P₂,P₃Being a real matrix, a scalar quantity₁>0,₂>0，r_dThe derivative for r (t) represents the rate of change, r (t)_maxDenotes the maximum value of the propagation delay, r, under specific network conditions Representing the upper limit of the propagation delay, I being the identity matrix, P₁，P₂，P₃Q and R are solutions of formula (14);

step4 setting the parameters for establishing equation (14) includes the step of setting α_i，β_iValue range α_i∈[a_αi，b_αi]，β_i∈[a_βi，b_βi]Step size of searchN ∈ N, N being a non-zero set of natural numbers;

inputting: a is_αi,b_αi,a_βi,b_βi,r_min=1,i=1,2,...,k;

Step 1: let i =1;

step2 setting α_i=a_αi,i=1,2,...,k;

Step3 setting β_i=a_βi,i=1,2,...,k;

Step 4: calculating P according to the formula (14)_1i,P_2i,P_3i,Q_i,R_i,_1i,_2i,r_i(ii) a If P is_1i,P_2i,P_3i,Q_i,R_i,_1i,_2i,r_iExist, and r is_i<r_minExecuting S5; if P is_1i,P_2i,P_3i,Q_i,R_i,_1i,_2i,r_iAbsent, go to S6;

step 5: let r be_min=r_i，A jump is made to the step S6,r_dmin，p when i =1,2, k, i is the current value, respectively_1i，P_2i，P_3i，Q_i，_1i，_2i，α_i，β_i，r_di，R_iThe cached output value of (a);

step 6: is provided withIf β_i≤b_βiGo to Step4, otherwise, let β_i=a_βiGo to Step 7;

step7 setting α_i=a_αi+h_αiIf α_i≤b_αiStep3, otherwise, i = i +1, Step 2;

step8, outputting P when i is correspondingly taken in i =1,2_1i，P_2i，P_3i，Q_i，_1i，_2i，α_i，β_i，r_i,R_iIs buffered to output valuer_min，

And 5: pairing a mobile ad hoc network node i with a transmission traffic rate x_iIs set toNode i employs the sending traffic rate x_iSensitivity to queuing delay is set toThe capacity stability of the mobile ad hoc network is controlled.

Compared with the prior art, the invention has the following advantages:

1. aiming at the capacities of MANETs, the influence of time-varying propagation delay related conditions on the stability of the MANETs is researched for the first time, a novel stability control algorithm related to MANETs capacity non-cooperative programming game delay is provided by combining a descriptor with a Lyapunov-Krasovski functional method, a discrete delay descriptor is used as a neutral model transformation technology based on no additional dynamics discussion, and the method is a powerful tool for analyzing the stability of a nonlinear dynamic time-delay related system and enabling the obtained decision criterion to have small conservatism.

2. The obtained method for controlling the capacity stability of the MANETs related to the propagation delay has universality for the MANETs adopting a non-competitive conflict-free MAC protocol, can be achieved by only adjusting the physical properties of MANETs nodes, such as the adopted power, the available memory size, a signal modulation method, a coding mode and the like, and provides powerful theoretical support for guiding the construction of the MANETs meeting the QoS.

3. The calculation amount is small, and the control condition of the propagation delay related capacity stability can be obtained only by utilizing an MATLAB tool box.

4. The descriptor technology is combined with an LMI method to analyze the stability of an MANETs capacity analysis model which is based on a conflict-free shared single channel and considers time-varying propagation delay correlation in normalized time, and a uniform capacity stability control framework with small conservation is established for MANETs adopting a non-competitive conflict-free MAC protocol.

5. The stability control method obtained by the invention is under the time delay related condition, and the control index obtained by calculation is the maximum value of the propagation time delay, so that the operability is stronger and the conservation is weaker.

Drawings

Fig. 1 is a network topology configuration diagram of embodiment 1.

Fig. 2a is a diagram of the sending flow rate of the Node1 in embodiment 1 when the control method of the present invention is not used for control;

fig. 2b is a flow rate diagram sent by the Node2 in embodiment 1 when the control method of the present invention is not used for control.

Fig. 3a is a graph of sending traffic stability by the Node1 and the Node2 in embodiment 1 after algorithm control is adopted.

FIG. 3b is a graph of capacity stability in example 1 after algorithm control.

Fig. 4 is a network topology structural diagram of embodiment 2.

Fig. 5a is a diagram of the sending flow rate of the Node1 in embodiment 2 when the control method of the present invention is not used for control.

Fig. 5b is a flow rate diagram sent by the Node2 in embodiment 2 when the control method of the present invention is not used for control.

Fig. 5c is a flow rate diagram sent by the Node3 in embodiment 2 when the control method of the present invention is not used for control.

Fig. 6a is a graph of sending traffic stability by the Node1, the Node2 and the Node3 in embodiment 2 after algorithm control is adopted.

FIG. 6b is a graph of capacity stability in example 2 after algorithm control.

Fig. 7a is a diagram of sending traffic stability of Node1, Node2 and Node3 in embodiment 3 under TDMA and DSR protocols.

Figure 7b is a graph of capacity stability in example 3 under TDMA, DSR protocols.

Fig. 8a is a diagram of sending traffic stability by the Node1, the Node2 and the Node3 in embodiment 3 under the TDMA and AODV protocol.

Fig. 8b is a graph of capacity stability in example 3 under TDMA, AODV protocol.

Detailed Description

The technique of the present invention will be described in further detail with reference to the drawings and examples.

A method for controlling the stability of a time delay related mobile ad hoc network is characterized by comprising the following specific steps:

step 1: establishing a MANETs capacity analysis non-cooperative planning game model as shown in a formula (9),

i=1,2,...,k,m=1,2,...,j,h=1,2,...,k；

equation (9) is a nonlinear time-varying time-lag differential equation, and in order to analyze (9) without introducing additional kinetic discussion, the following identity transformation is performed on (9) to equation (10):

equation (9) is equivalent to equation (10) for a descriptor system with discrete and distributed delay terms, which will not lead to any additional kinetic discussion for the stability analysis of the original model (9) and reduce the conservatism of the obtained conclusions; wherein, C represents a constant, is an empirical value, and can be obtained from actual network performance, x (t) represents a sending traffic rate vector of the mobile ad hoc network source node, x (t-r (t)) represents a sending traffic rate vector of the mobile ad hoc network source node added with a propagation delay term, and representing the vector quantity of the rate of change of the sending traffic rate of the source node of the mobile ad hoc network, y (t) has the same meaningx_iI =1, 2.. k denotes the rate at which data traffic is sent by source node i,h =1, 2.. k denotes the traffic rate x sent by the source node i_iOver a linkH, flow rate of(t) represents the time at which the link is traversedThe h-th traffic rate of (2),representing a transit linkThe sum of the flow rates of (a) and (b),(t) represents the time at which the link is traversedThe sum of the flow rates of (a) and (b),(t-r (t)) represents the time of delay r (t) at time t passing through the linkSum of flow rates of (a), x_iK denotes the rate at which the source node i sends data traffic, α_iRepresenting node i vs. the transmit traffic rate x_iDegree of sensitivity of β_iIndicating that node i employs the sending traffic rate x_iThe degree of sensitivity to the queuing delay,indicating assignment to a linkThe ratio of the time of (a) to (b),represents a link l_iTo be fixedConstant volume, t represents network running time, r (t) represents that the sending flow rate of the node i is x_iIs passed through the linkm =1, 2.. times, j, j is the number of links of the mobile ad hoc network, the resulting time-varying propagation delay, s_{m}Representing a feasible link set of a concurrency scene, and K represents a source node set;means that when i =1,2,. k, m =1,2,. j,andthe minimum value of the products is the minimum value,representing the ratio of time allocated to link m.

The specific process of establishing MANETs capacity analysis non-cooperative planning game model formula (9) is as follows:

the evolution equation of the sending flow rate of the MANETs source node of the distributed time-varying dynamic system without considering the time delay is shown as a formula (5).

i=1,2,...,k,m=1,2,...,j,h=1,2,...,k,ω∈R⁺And is constant, α_iRepresenting node i vs. the transmit traffic rate x_iThe sensitivity degree of the node i is determined by the power adopted by the node i, the size of the available memory, the signal modulation method, the coding mode, the link bandwidth connected with the node i, the routing strategy and other factors β_iIndicating that node i employs the sending traffic rate x_iSensitivity to queuing delay.

In equation (5), consider the simplest case: take ω =1, and becauseIndicating that source node i adopts sending flow rate x in MANETs non-cooperative planning game_iThe link accumulated rate of change in revenue in the sense of proportional fairness is only in the cost term of its game-so the queuing delay rate of change term β_i Taking into account the time-varying propagation delay. At this time, x_iShould be a function of t, i.e. x_i(t), let r (t) denote that the node i sends the flow rate as x_i(t) data flow over the linkThe time-varying propagation delay produced by m =1, 2.. times.j, the queuing delay rate of change term can be written as β_i Wherein r (t) represents that the sending flow rate of the node i is x_iIs passed through the linkThe time-varying propagation delay produced by m =1, 2.. times.j is a function of t, and 0 ≦ r (t ≦ r) ,r ,r_dIs constant, at the same time, is examinedFurther, the influence of r (t) is equally transformed to β_i The MAN is obtained that takes into account the time-varying propagation delayETs capacity analysis non-cooperative planning game model source node sending flow rate evolution equation set is as formula (9):

i=1,2,...,k,m=1,2,...,j,h=1,2,...,k

simple notes

Then

Reissue to order

f(x(t))=[f₁(x(t))f₂(x(t))...f_k(x(t))]^T

g(x(t-r(t)))=[g₁(x(t-r(t)))g₂(x(t-r(t)))...g_k(x(t-r(t)))]^T

Then formula (5) is equivalent to formula (11)

Equation (11) may further transform the fast variables y (t) identity into a descriptor system with discrete and distributed delay terms

And step 3: the conditions for gradually stabilizing the descriptors of the MANETs capacity analysis non-cooperative planning game model established in the step2 comprise a condition (13) and a condition (14),

whereinTheta is not less than 0 andθ is a given constant;

wherein,Ω₁₂=P₁-P₂ ^T+C^TP₃，

Ω₂₂=-P₃-P₃ ^T+r R；P₁=P₁ ^T>0,Q=Q^T>0, is a positive definite real symmetric matrix, P₂,P₃Being a real matrix, a scalar quantity₁>0,₂>0，r_dThe derivative for r (t) represents the rate of change, r (t)_maxDenotes the maximum value of the propagation delay, r, under specific network conditions Representing the upper limit of the propagation delay, I being the identity matrix, P₁，P₂，P₃Q and R are solutions of formula (14).

The nonlinear term f (x (t)) of the formula (11), g (x (t-r (t)) satisfy the constraint condition (12) under the constraint of the formula (4),

wherein,if θ ≧ 0 is a given constant, then constraint (12) can also be written as equation (13):

the formula (4) is:

representing a predetermined set of routing linksMinimum capacity of α_iRepresenting node i vs. the transmit traffic rate x_iThe sensitivity degree of the node i is determined by the power adopted by the node i, the size of the available memory, the signal modulation method, the coding mode, the link bandwidth connected with the node i, the routing strategy and other factors β_iIndicating that node i employs the sending traffic rate x_iSensitivity to queuing delay.

The establishment procedure of equation (4) is as follows:

in the MANETs with n nodes and j links in the normalized time, if the largest feasible link which can be simultaneously concurrent and has no mutual interference existsCollection S_maxAnd S is_maxTo satisfy the feasible scheduling link set of equation (1), then the MANETs capacity isWhere K represents a set of source nodes, x_i>0, i =1, 2.. k denotes the rate at which traffic is sent by the source node i, m =1, 2.. j denotes the number of links, { x ·^* ₁,x^* ₂,...,x^* _kDenotes the Nash equalization solution.

The link scheduling set that satisfies the time allocation of equation (1) is called the feasible scheduling link set of MANETs:

wherein s is_{m}Represents a set of feasible links that can be used in a concurrent scenario,representing a feasible set of links (a scenario of all concurrently available links) within normalized time 1,representing the ratio of time allocated to link m. The feasible scheduling link set obtaining method adopts a non-cooperative planning game model for mobile Ad hoc network capacity analysis (the non-cooperative planning game model for mobile Ad hoc network capacity analysis, Poplar, Yangdan, Zhao hong, Gewangxin, university of south China university of academic Press (Nature science edition) 12 months in 2010, volume 38, period 12, 61-72)

x^* _iNon-cooperative programming game G as in formula (2) for game node (source node) i in sending traffic rate x_iOf (2) a policy space omega_iWithin a range of valuesThe maximum utility function under the constraint of (3) is calculated as Nash equilibrium solution { x^* ₁,x^* ₂,...,x^* _kAnd (6) balancing the flow rate of the Nash of the source node i.

G={K,{Ω_i},{u_i(x_i)}},i=1,2,...,k （2）

Wherein,h =1, 2.. k denotes a transit linkThe h-th traffic rate of (2),representing a transit linkThe sum of the flow rates of the two, in an ideal situation,therefore omega_iCan be represented by formula (4):

representing a predetermined set of routing linksMinimum capacity of u_i(x_i) Representing the source node i traffic rate assignment utility function, α_iRepresenting node i vs. the transmit traffic rate x_iIs sensitive toThe degree is determined by the power adopted by the node i, the size of the available memory, the signal modulation method, the coding mode, the link bandwidth connected with the node i, the routing strategy and other factors β_iIndicating that node i employs the sending traffic rate x_iThe degree of sensitivity to the queuing delay,indicating assignment to a linkThe ratio of the time of (a) to (b),represents a link l_iA fixed capacity of (a).

The following form, the Lyapunov-Krasovskii functional, was constructed:

V(t)=V₁(t)+V₂(t)+V₃(t) （15）

the first term of equation (15) corresponds to the descriptor system, the second term being introduced for latency independent conditions that account for discrete latency r (t), and the third term being introduced for latency dependent conditions that account for latency r (t).

Calculating the derivative of V (t) along the system (15) to obtain:

obtained by the formula (1):

thus, there are

Wherein,

（15）

wherein omega₀₁₁=P₂ ^TC+C^TP₂+Q；

Ω₀₁₂=Ω₁₂=P₁-P₂ ^T+C^TP₃；

Ω₀₂₂=Ω₂₂=-P₃-P₃ ^T+r R；

It is clear that for any λ (t) ≠ 0 (Note 1),possibly equal to 0, even if a positive definite symmetric matrix P is present₁Q and R and the real matrix P₂,P₃So thatWe can also only obtain semi-positive conditions for the system (9), i.e.And the system (9) is asymptotically stable under the condition that a positive definite symmetric matrix P exists₁Q and R and the real matrix P₂,P₃So thatTo this end, we use the S-procedure construction system (9) to asymptotically stabilize the relaxation condition as long as there is a scalar quantity₁>0,₂>0, such that the following holds:

therefore, for all λ (t) ≠ 0, if there is a positive definite symmetric matrix P₁Real matrices of Q and R P₂,P₃Scalar quantity₁>0,₂>0, so that the LMI (14) formula holds, the dynamic system (9) is asymptotically stable.

It is clear that λ (t) ≠ 0 is equivalent to (x)^T(t)x^T(t-r (t))) > 0, in fact, if (x)^T(t)x^T(t-r (t)) =0, then f (x (t)) =0 and g (x (t-r (t)) =0, then from system (10), the results are obtainedThus λ (t) = 0.

Equation (4) provides a time delay-dependent stability criterion for a nonlinear time-varying delay system with nonlinear terms in terms of a feasible solution using an LMI technique.

Due to α in (9)_i,β_iAs the undetermined coefficient, as long as P satisfying the condition can be obtained, as can be seen from the formula (4)₁,P₂,P₃,Q,R,₁,₂Is present and makes r Minimum α_i,β_iThe capacity of non-cooperative game games considering time-varying propagation delay can be stabilized, and α is obtained_i,β_iNot unique within its effective value range, so that P satisfying the condition can be taken₁,P₂,P₃,Q,R,₁,₂Is present and r =r_dminα of (1)_i，β_i。

And 4, step 4: setting upr_min，The following steps may be employed:

setting α_i，β_iValue range α_i∈[a_αi，b_αi]，β_i∈[a_βi，b_βi]Step size of searchN ∈ N, N being a non-zero set of natural numbers;

inputting: a is_αi,b_αi,a_βi,b_βi,r_min=1,i=1,2,...,k;

Step 1: let i =1;

step2 setting α_i=a_αi,i=1,2,...,k;

Step3 setting β_i=a_βi,i=1,2,...,k;

Step 4: calculating P according to the formula (14)_1i,P_2i,P_3i,Q_i,R_i,_1i,_2i,r_i(ii) a If P is_1i,P_2i,P_3i,Q_i,R_i,_1i,_2i,r_iExist, and r is_i<r_minExecuting S5; if P is_1i,P_2i,P_3i,Q_i,R_i,_1i,_2i,r_iAbsent, go to S6;

step 5: order toA jump is made to the step S6,r_dmin，p when i =1,2, k, i is the current value, respectively_1i，P_2i，P_3i，Q_i，_1i，_2i，α_i，β_i，r_di，R_iThe cached output value of (a);

step 6: is provided withIf β_i≤b_βiGo to Step4, otherwise, let β_i=a_βiGo to Step 7;

step7 setting α_i=a_αi+h_αiIf α_i≤b_αiStep3, otherwise, i = i +1, Step 2;

step8, outputting P when i is correspondingly taken in i =1,2_1i，P_2i，P_3i，Q_i，_1i，_2i，α_i，β_i，r_i,R_iIs buffered to output valuer_min，

And 5: pairing a mobile ad hoc network node i with a transmission traffic rate x_iIs set toNode i employs the sending traffic rate x_iSensitivity to queuing delay is set toThe capacity stability of the mobile ad hoc network is controlled.

Example 1: it is set that in the wireless MANETs, there are 3 nodes, Node1, Node2, Node3 and two links Having capacity values ofThe scheduling time of the link in the normalized time is respectivelyThere is a traffic rate x sent by Node1 to Node3 in the network₁The traffic rate sent by Node2 to Node3 is x₂Let α_i,β_iThe value range is α₁∈[110],α₂∈[110],β₁∈[18],β₂∈[18]The network topology is as shown in figure 1.

If the method provided by the invention is not adopted for calculation α_i,β_iStability control for MANETs capacity at α_i,β_iAny value within the value range (as shown in table 1),then Node1 and Node2 sending flow rate graphs as shown in fig. 2a and 2b are obtained, and it is obvious that the network capacity can not reach a steady state.

TABLE 1

Then, a control method of the stability of the time delay correlation mobile self-organizing network is adopted to calculate:

₁=1.7961×10⁴,₂=1.9082×10⁶

and r_min=5.0×10^-6Then, α at this time is obtained_i,β_i(see table 2), substituting into MANETs capacity analysis non-cooperative planning game model formula (9), simulating MANETs as shown in fig. 1, wherein the simulation time is in seconds (S) and the sending traffic rate of the source Node is updated every 1S, so as to obtain the Node1, Node2 sending traffic rate graph and network capacity graph as shown in fig. 3a and 3 b.

As can be seen from FIGS. 3a and 3b, the sending flow rates of the source Node1 and Node2 converge to the equilibrium point within less than 10.2s, and the capacities of the MANETs reach the stable capacity within 5.3s, which verifies that the control method of the present invention has good stability control effect on the topology shown in FIG. 1, so that I can be within the physical performance range of the MANETs (i.e. α)_i,β_iI =1,2 within the valid value range), adjust α_i,β_iAnd i =1,2 values are used for carrying out stability control on capacity and optimizing and distributing the rate of sending flow of each source node so as to fully utilizeNetwork resources, and the network capacity is maximized.

TABLE 2

Example 2: it is set up that there are 4 nodes Node1, Node2, Node3, Node4 and 3 links in the MANETsHaving capacity values ofThere is a traffic rate x sent by Node1 to Node3 in the network₁Traffic rate x Node2 sends to Node3₂And traffic rate x that Node3 sends to Node4₃Wherein x is₁And x₂Simultaneous transmission, normalizing the set of feasible links within time 1The scheduling time of each link in the normalized time is respectivelyLet α_i,β_iThe value range is α₁∈[110],α₂∈[115],α₃∈[115]，β₁∈[110],β₂∈[115],β₃∈[115]. The network topology is shown in fig. 4.

If the control algorithm of the present invention is not used to calculate α_i,β_iThe capacity is subjected to stability control at α_i,β_iAny value in the range (as table 3) can be obtained to obtain the Node1, Node2, Node3 sending flow rate diagrams as shown in fig. 5a, 5b and 5c, which shows that the MANETs capacity can not reach the stable state.

TABLE 3

Then, the control algorithm provided by the invention calculates:

₁=10⁴×3.1327,₂=10⁴×7.1973

and r_min=1.5×10^-6Then, α at this time is obtained_i,β_i(see table 4), MANETs capacity analysis non-cooperative programming game model (9), simulation MANETs as shown in fig. 4, simulation time is in seconds (S) unit, updating the sending flow rate every 1S source Node, get the sending flow rate diagram of Node1, Node2, Node3 and network capacity diagram as shown in fig. 6a and 6b, it can be seen from fig. 6a and 6b that the sending flow rates of source Node1, Node2, Node3 converge to the balance point when less than 7.0S, and MANETs capacity also reaches stable capacity within 7.1S_i,β_iI =1,2,3 within the effective value range), adjust α_i,β_iAnd the values of i =1,2 and 3 control the stability of the capacity, and optimize and distribute the rate of sending flow of each source node so as to fully utilize network resources and maximize the network capacity.

TABLE 4

Example 3: to further verify the performance of the control algorithm provided by the invention, after the control method is adopted to perform stability control in embodiment 2, a simulation network is established on an OPNET14.5 platform, and a wlan-roaming track of a mobile node is assumed to be 10²Moving within the km range, the MAC layer adopts a TDMA protocol, the routing layer adopts AODV and DSR protocols respectively, and the values of other parameters are the same as those in embodiment 2. The results are shown in FIGS. 7a, 7b, 8a and 8 b. It can be seen from the experimental results that although the MANETs capacity takes longer to converge to the steady state than in example 2, the capacity can converge to the steady state under different routing protocols. The reason for analyzing the long convergence time (10.8 s) under the DSR protocol is that under the same network condition, the end-to-end delay under the DSR protocol is larger than that of the AODV.

The modeling method and the analysis means used by the invention have wide applicability, and the stability control can be carried out on a large class of network capacity stability control problems by referring to the control method provided by the invention.

Finally, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A method for controlling the stability of a time delay related mobile ad hoc network is characterized by comprising the following specific steps:

step 1: establishing a MANETs capacity analysis non-cooperative planning game model as shown in formula (9), wherein the MANETs are mobile ad hoc networks,

step 2: the MANETs capacity analysis non-cooperative planning game model in the step1 is analyzed, the expression (9) is equivalent to the descriptor expression (10),

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=y\left(t\right)\\ 0=-y\left(t\right)+Cx\left(t\right)-Cx(t-r(t\left)\right)-C\underset{t-r\left(t\right)}{\overset{t}{\&Integral;}}y\left(\mathrm{\&xi;}\right)d\mathrm{\&xi;}+Af\left(x\right(t\left)\right)+Bg\left(x\right(t-r\left(t\right)\left)\right)\end{array}\right.---\left(10\right)$

wherein, C represents constant and can be obtained from actual network performance, x (t) represents the sending flow rate vector of the source node of the mobile self-organizing network, x (t-r (t)) represents the sending flow rate vector of the source node of the mobile self-organizing network added with the propagation delay item, andrepresenting the source node of the mobile self-organizing network to send a traffic rate change vector, y (t) has the same meaning

f(x(t))＝[f₁(x(t)) f₂(x(t))...f_i(x(t))...f_k(x(t))]^TK, k < n, n being the number of nodes of the ad-hoc network, wherein,

g(x(t-r(t)))＝[g₁(x(t-r(t))) g₂(x(t-r(t)))...g_i(x(t-r(t)))...g_k(x(t-r(t)))]^Tk, wherein,

a and B are diagonal matrixes, and specifically are as follows:

representing the source node i of the mobile ad hoc network sending a traffic rate change rate vector,representing the traffic rate x sent by the source node i_iOver a linkThe number h of (a) is,representing a transit linkThe sum of the flow rates of (a) and (b),indicating the passage of a link at time tThe sum of the flow rates of (a) and (b),representing the transit of the link at a delay r (t) of time tSum of flow rates of α_iRepresenting node i vs. the transmit traffic rate x_iDegree of sensitivity of β_iIndicating that node i employs the sending traffic rate x_iThe degree of sensitivity to the queuing delay,indicating assignment to a linkThe ratio of the time of (a) to (b),represents a link l_iT represents the network running time, r (t) represents the node i sending traffic rate x_iIs passed through the linkThe resulting time-varying propagation delay, s_{m}Representing a feasible link set of a concurrency scenario, K representing the number of source nodes, j being the number of links of the mobile ad hoc network, K representing the source node set,expression solutionAndthe minimum of the products of (a);

and step 3: the conditions for gradually stabilizing the descriptors of the MANETs capacity analysis non-cooperative planning game model established in the step2 comprise a condition (13) and a condition (14),

whereinAnd isθ is a given constant;

$\left[\begin{array}{cccccc}{\mathrm{\&Omega;}}_{11}& {\mathrm{\&Omega;}}_{12}& -{P_2}^{T}C& -r_{\mathrm{\&Gamma;}}{P}_2^{T}C& {P_2}^{T}A& {P_2}^{T}B\\ {{\mathrm{\&Omega;}}_{12}}^T& {\mathrm{\&Omega;}}_{22}& -{P_3}^{T}C& -r_{\mathrm{\&Gamma;}}{P}_3^{T}C& {P_3}^{T}A& {P_3}^{T}B\\ -C^T{P}_2& -C^T{P}_3& -(1-r_d)Q+{\mathrm{\&epsiv;}}_2{\mathrm{\&theta;}}^{2}I& 0& 0& 0\\ -r{\left(t\right)}_{\max }{C}^T{P}_2& -r_1{C}^T{P}_3& 0& -(1-r_d)r_{\mathrm{\&Gamma;}}R& 0& 0\\ A^T{P}_2& A^T{P}_3& 0& 0& -{\mathrm{\&epsiv;}}_{1}I& 0\\ B^T{P}_2& B^T{P}_3& 0& 0& 0& -{\mathrm{\&epsiv;}}_{2}I\end{array}\right]<0---\left(14\right);$

wherein,Ω₁₂＝P₁-P₂ ^T+C^TP₃，Ω₂₂＝-P₃-P₃ ^T+r R；P₁＝P₁ ^T＞0，Q＝Q^T> 0, is a positive definite real symmetric matrix, P₂，P₃Being a real matrix, a scalar quantity₁＞0，₂＞0，r_dThe derivative for r (t) represents the rate of change, r (t)_maxDenotes the maximum value of the propagation delay, r, under specific network conditions Representing the upper limit of the propagation delay, I being the identity matrix, P₁，P₂，P₃Q and R are solutions of formula (14);

the nonlinear term f (x (t)) of the formula (11), g (x (t-r (t)) satisfy the constraint condition (12) under the constraint of the formula (4),

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}\left(t\right)=y\left(t\right)\\ y\left(t\right)=Af\left(x\right(t\left)\right)+Bg\left(x\right(t-r\left(t\right)\left)\right)\end{array}\right.---\left(11\right)$

wherein,given a constant, the constraint (12) can also be written as equation (13):

the formula (4) is:

$\left\{{x^h}_{i,l_{i_m}}\right|x_{l_{i_m}}=\underset{h\&Element;K}{\&Sigma;}{x^h}_{i,l_{i_m}}<t_{s_{l_{i_m}}}{g}_{l_i},i=1,2,\mathrm{...},k,m=1,2,\mathrm{...},j\}---\left(4\right);$

step4 setting the parameters for establishing equation (14) includes the step of setting α_i，β_iValue range α_i∈[a_αi，b_αi]，β_i∈[a_βi，b_βi]Step size of searchN ∈ N, N being a non-zero set of natural numbers;

inputting: a is_αi，b_αi，a_βi，b_βi，

S1: setting i to be 1;

s2 setting α_i＝a_αi，i＝1，2，...，k；

S3 setting β_i＝a_βi，i＝1，2，...，k；

S4: calculating P according to the formula (14)_1i，P_2i，P_3i，Q_i，R_i，_1i，_2i，r_i(ii) a If p is_1i，P_2i，P_3i，Q_i，R_i，_1i，_2i，r_iExist, and r is_i＜r_minExecuting S5; if P is_1i，P_2i，P_3i，Q_i，R_i，_1i，_2i，r_iAbsent, go to S6;

s5: let r be_min＝r_i，A jump is made to the step S6,p is the current value of i ═ 1,2_1i，P_2i，P_3i，Q_i，_1i，_2i，α_i，β_i，r_di，R_iThe cached output value of (a);

s6 setting β_i＝a_βi+h_βiIf β_i≤b_βiGo to S4, otherwise, turn to β_i＝a_βiGo to S7;

s7 setting α_i＝a_αi+h_αiIf α_i≤b_αiTurning to S3, otherwise i ═ i +1; turning to S2;

s8: output P when i is taken as 1,2_1i，P_2i，P_3i，Q_i，_1i，_2i，α_i，β_i，r_i，R_iIs buffered to output value

And 5: pairing a mobile ad hoc network node i with a transmission traffic rate x_iIs set toNode i employs the sending traffic rate x_iSensitivity to queuing delay is set toThe capacity stability of the mobile ad hoc network is controlled.