Saturation Control Method of Communication Network System Based on Linear Programming

Abstract

The present invention discloses a saturation control method for a communication network system based on linear programming. The method first establishes a state space model of a singular switching positive system of a communication network system, then constructs a saturation controller of the communication network system, and further proposes the conditions for the smooth operation of the communication network saturation control system based on linear programming, while ensuring the positivity and stability of the communication network saturation control system. The method uses a singular switching positive system to establish a state space model of a communication network saturation control system, and designs a saturation control method based on linear programming to ensure that the system can still operate smoothly under residence time restriction switching. Through experiments, it is confirmed that the saturation control method proposed by the present invention can effectively improve the resource utilization rate of the communication network system, optimize the performance of the communication network system, and further improve the control efficiency of the communication network system. This is of great significance to both control theory and practical application.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control, and relates to a communication network system saturation control method based on linear programming, which can be applied to urban data communication transmission systems. Background Art

[0002] The communication network system is an important system for urban data transmission, local information connection or wireless information transmission. However, with the rapid development of modern urban society, the requirements for the transmission efficiency of information and data are gradually increasing. During the construction process of the communication network system, it is necessary to select a suitable communication system according to the specific situation to improve the efficiency of information transmission. There are many factors that affect the selection of the communication system, such as the resource allocation between the various subsystems, and the trade-off between the performance and energy consumption of the subsystems. If these problems cannot be handled reasonably, it will bring inconvenience to urban development and people's lives. Therefore, it is very necessary and critical to design a communication network saturation control system that can flexibly switch the data transmission system.

[0003] In the communication system, since the amount of information transmitted at different times is always non-negative, the communication control system meets the characteristics of a positive system. Since the amount of information transmitted in different areas of the city is different, a communication subsystem with multiple modes can be constructed. Therefore, it is appropriate to use a switching positive system to model this type of actual system. When using a switching positive system for modeling, if the communication control system is modeled based on a continuous-time switching positive system, the demand for information in each area can be effectively observed and adjusted in time, thereby improving the data resource allocation rate. However, modeling using a switching positive system cannot truly and accurately estimate the actual situation, which is quite different from the actual situation, and resources cannot be reasonably allocated, affecting communication efficiency. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a communication network system saturation control method based on linear programming. When modeling, a singular switching positive system is selected for modeling, which solves the problem that the switching positive system modeling cannot accurately determine the demand for communication data in various areas of the city, and the error is large compared with the actual demand.

[0005] The communication network system saturation control method based on linear programming has the following specific steps:

[0006] Step 1: Establish the state space model of the communication network saturation control system:

[0007]

[0008] where · represents the first-order derivative, x(t)∈R n ,u(t)∈R qare the system state and control input of the communication network saturation control system in continuous time, \(t\) represents time, and \(R\) * denotes a column vector of length \(*\). \(sat(·)\) represents the saturation term of the communication network saturation control system. The function \(\sigma(t)\) represents the switching signal of the continuous-time subsystem, and its values are all within the finite set \(S = \{1, 2, \ldots, N\}\), where \(N\) is a positive constant. For simplicity, it is defined that \(\sigma(t)=i\) when the \(i\)-th continuous-time subsystem is activated. Assume that in the continuous-time subsystem, \(A\) i is a Metzler matrix, \(B\) i \(\geq0\), where \(A\) i \(\in R\) n×n , \(B\) i \(\in R\) n×q , \(E\in R\) n×n , the rank of the singular matrix \(E\) is \(r\), \(r < n\). For convenience, we split the matrices \(A\) i , \(B\) i and \(E\) into \(B\) i \(=[B\) i1 \(B\) i2 , where \(A\) i1 \(\in R\) r×r , \(A\) i2 \(\in R\) r×(n-r) , \(A\) i3 \(\in R\) (n-r)×r , \(A\) i4 \(\in R\) (n-r)×(n-r) , \(A\) i4 has a non-zero determinant value, \(B\) i1 \(\in R\) r×q , \(B\) i2 \(\in R\) (n-r)×q . \(R\) *×* denotes a matrix of size \(*\times*\).

[0009] Step 2: Construct the saturation controller of the communication network system:

[0010] \(u(t)=K\) σ(t) \(x(t)\) (2)

[0011] where \(K\) σ(t) is the controller gain matrix of the continuous-time subsystem.

[0012] Step 3: Design the conditions for the smooth operation of the communication network saturation control system under dwell-time constraints as follows:

[0013] Design constants \(\alpha>0\), \(\gamma>0\), \(0 < \xi < 1\), for any \((i, j)\in S\), \(i\neq j\), the minimum dwell time The matrix \(D\) of size \(R\) q×q iz ​is a diagonal matrix whose diagonal elements are either 0 or 1, z∈{0,1,...,2 q}, define the vector The size is R n ; ν i,s ≥0, The size is R n , where s∈{0,1,…,S}, m∈{0,1,…,q}.

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] v i,0 -v j,s ≤0 (14)

[0026]

[0027]

[0028]

[0029]

[0030] For any (i, j)∈S, i≠j, then, under the saturation controller in step 2, the communication network control system in step 1 is positive and has L 1 The stability of the gain performance. Saturation control gain matrix K i,s and the auxiliary gain matrix H i,s The specific form of the design is:

[0031]

[0032]

[0033] And the residence time method selects the minimum residence time method, and the switching condition meets:

[0034]

[0035] Among them, K i,s =[K i1,s K i2,s ]、H i,s =[H i1,s H i2,s ]、 e q represents an r-dimensional column vector whose elements are all 1, It represents an r-dimensional column vector whose m-th element is 1 and the rest of the elements are 0. The superscript T represents the transpose of a vector or matrix.

[0036] The present invention has the following beneficial effects:

[0037] The present invention uses a continuous-time linear cosine Lyapunov function to design a saturation control method based on linear programming, so that the communication network system can operate stably under the switching of residence time restrictions. The communication network control system using this saturation control method can effectively adapt to the changes in demand in different cities and reduce the conservatism of system performance utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of a communication network saturation control system;

[0039] Figure 2 It is a schematic diagram of the saturation controller framework for a singular switched positive system;

[0040] Figure 3 It is a schematic diagram of simulation results obtained by modeling using a switched positive system;

[0041] Figure 4 It is a schematic diagram of the simulation results obtained by modeling a singular switched positive system. DETAILED DESCRIPTION

[0042] The present invention is further described below in conjunction with specific embodiments, but the present invention is not limited to these specific embodiments. Those skilled in the art should recognize that the present invention covers all possible alternatives, improvements and equivalents within the scope of the claims.

[0043] This embodiment provides a saturation control method for a communication network system based on linear programming. For the Figure 1 shown communication network, a saturation controller as shown in Figure 2 is modeled, and the specific steps are as follows:

[0044] Step 1: Establish the state-space model of the communication network saturation control system:

[0045]

[0046] where · represents taking the first derivative, x(t) ∈ R n is an n*1 column vector, u(t) ∈ R q is a q*1 column vector, which respectively represent the system state and control input of the communication network saturation control system in continuous time, and t represents time. sat(·) is the saturation term of the communication network saturation control system. The function σ(t) represents the switching signal of the continuous-time subsystem, and its values are all within the finite set S = {1, 2,..., N}, where N is a positive constant. For simplicity, it is defined that σ(t) = i when the i-th continuous-time subsystem is activated. Assume that in the continuous-time subsystem, A i is a Metzler matrix, B i ≥0, where A i ∈R n×n , B i ∈R n×q , E ∈ R n×n , the rank of the singular matrix E is r, and r < n. For convenience, we split the matrices A i , B i and E into B i = [B i1 B i2 , where A i1 ∈R r×r , A i2 ∈R r×(n-r) , A i3 ∈R (n-r)×r , A i4 ∈R (n-r)×(n-r) , the determinant value of A i4 is not 0, B i1 ∈R r×q , B i2 ∈R (n-r)×q .

[0047] Step 2: Construct the saturation controller of the communication network system, and its construction form is as follows:

[0048] u(t) = K σ(t) x(t) (2)

[0049] Among them, K σ(t) is the controller gain matrix for the continuous-time subsystem.

[0050] Step 3: Design the conditions for the stable operation of the communication network saturation control system under the switching of residence time limit as follows:

[0051] Design constants α>0, γ>0, 0<ξ<1, for any (i,j)∈S, i≠j, the minimum residence time Size R q×q The matrix D iz is a diagonal matrix whose diagonal elements are either 0 or 1, z∈{0,1,…,2 q}, define the vector The size is R n ; vector ν i,s ≥0, The size is R n , where s∈{0,1,...,S}, m∈{0,1,...,q},

[0052]

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[0055]

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[0060]

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[0062]

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[0064] v i,0 -v j,s ≤0 (14)

[0065]

[0066]

[0067]

[0068]

[0069] Under the saturated controller in step 2, the communication network control system in step 1 is positive and has L 1 The stability of the gain performance. Saturation control gain matrix K i,s and the auxiliary gain matrix H i,s The specific form of the design is

[0070]

[0071]

[0072] And the residence time method selects the minimum residence time method, and the switching condition meets:

[0073]

[0074] Among them, K i,s =[K i1,s K i2,s ], H i,s =[H i1,s H i2,s ], e q represents an r-dimensional column vector whose elements are all 1, It represents an r-dimensional column vector whose m-th element is 1 and the rest of the elements are 0. The symbol T represents the transpose of a vector or matrix.

[0075] Step 4: The positive verification process of the communication network saturation control system is as follows:

[0076] Consider the positivity of the continuous-time subsystem: Using the continuous-time subsystem saturation controller in step 2, we can obtain

[0077]

[0078] Due to e q ≥0, B i ≥0, and ν i,s ≥0, so Using formulas (3) and (4) in step 3, we have

[0079]

[0080]

[0081] Combined with the continuous-time controller gain matrix K in step 3 i,s The specific form of

[0082]

[0083] Therefore, A i +B i K i is the Metzler matrix. Since E ≥ 0, for any non-negative initial condition, the continuous-time subsystem in step 1 is positive.

[0084] Step 5: The verification process of the stability of the communication network saturation control system is as follows:

[0085] Step 5.1, select the linear cosine Lyapunov function as

[0086] V(x(t))=x T (t)E T ν σ(t) (t) (26)

[0087] Among them, ν σ(t) > 0. Based on the minimum residence time, we will l ,t l+1 ) is divided into and In [t l ,t l+1 ) Time period design definition Then v i (t) can be expressed as:

[0088]

[0089] At the same time, you can get

[0090]

[0091] in

[0092] Step 5.2: First, consider When D iz and three different situations.

[0093] Step 5.2.1. Case 1: When D iz ≠I,

[0094]

[0095] According to (5) and (8) in step 3, we can conclude that:

[0096]

[0097] Step 5.2.2, Case 2: When D iz =I,

[0098]

[0099] According to (6) and (9) in step 3, we can conclude that:

[0100]

[0101] Step 5.2.3, Case 3: When D iz =0,

[0102]

[0103] According to (7) and (10) in step 3, we can conclude that:

[0104]

[0105] Step 5.3. Next, consider When D iz and three different situations.

[0106] Step 5.3.1. Case 1: When D iz ≠I,

[0107]

[0108]

[0109] According to (11) in step 3, we can conclude that:

[0110]

[0111] Step 5.3.2, Case 2: When D iz =I,

[0112]

[0113] According to (12) in step 3, we can conclude that:

[0114]

[0115] Step 5.3.3, Case 3: When D iz =0,

[0116]

[0117] According to step 3 (13), we can get:

[0118]

[0119] Step 5.4. Therefore, combining formula (29) in step 5.2 and formula (30) in step 5.3, we can conclude that:

[0120]

[0121] Step 5.5: Through step 5.4, we can conclude:

[0122]

[0123] The following equation is obtained by using the Lyapunov function in step 5.1:

[0124]

[0125] When t∈[t l-1 ,t l ), σ(t)=j, when t∈[t l ,t l+1 ), σ(t)=i.

[0126] Through step 3 (14), we can get:

[0127]

[0128] Step 5.6, finally we can conclude:

[0129]

[0130] Therefore, the communication network saturation control system has L 1 Gain stability.

[0131] Step 6: Use simulation to simulate the actual situation:

[0132] Given a set of parameters for system (1), they are Through the above steps, the controller gain matrices of the continuous-time subsystem are obtained as K 1,0 =[12.0038 15.1716], K 1,1 =[7.4628 8.4874], K 1,2 =[2.4771 2.4771]K 2,0 =[-3.8510 -0..2524], K 2,1=[-5.3909 -3.6824], K 2,2 =[-3.05008 -3.0508]At the same time, for the same parameters, the switching positive system is used to model and solve, and the simulation results are as follows Figure 3 , Figure 4 By comparing the simulation diagrams, it can be seen that when the singular switched positive system is used for modeling, the error reduction rate is smaller than the error reduction rate when the switched positive system is used for modeling, which proves that the singular switched positive system can better meet the needs of the actual situation.

Claims

1. A communication network system saturation control method based on linear programming, characterized in that: The specific steps are as follows: Step 1: Establish the state space model of the communication network saturation control system: in Indicates the first-order derivative, x(t)∈R n is an n*1 column vector, u(t)∈R q is a column vector of q*1, which respectively represents the system state and control input of the communication network saturation control system in continuous time, and t represents time; sat(·) is the saturation term of the communication network saturation control system; the function σ(t) represents the switching signal of the continuous time subsystem, and its value is within the finite set S={1,2,…,N}, where N is a positive constant; it is defined that σ(t)=i when the i-th continuous time subsystem is activated; Assume that A in the continuous-time subsystem i is a Metzler matrix, where A i ∈R n×n , B i ∈R n×q , E ∈ R n×n , the rank of the singular matrix E is r, r < n; split the matrices A i , B i and E into B i = [B i1 B i2 , where A i1 ∈R r×r , A i2 ∈R r×(n-r) , A i3 ∈R (n-r)×r , A i4 ∈R (n-r)×(n-r) , A i4 has a non-zero determinant value, B i1 ∈R r×q , B i2 ∈R (n-r)×q ; Step 2: construct a saturation controller for the communication network system, which is constructed as follows: u(t)=K σ(t) x(t) (2) Among them, K σ(t) is the controller gain matrix of the continuous-time subsystem; Step 3: Design the conditions for the stable operation of the communication network saturation control system under the switching of residence time limit as follows: Design constants α>0, γ>0, 0<ξ<1, for any (i,j)∈S, i≠j, the minimum residence time Size R q×q The matrix D iz is a diagonal matrix whose diagonal elements are either 0 or 1, z∈{0,1,…,2 q }, define the vector The size is R n ;vector The size is R n , where s∈{0,1,…,S}, m∈{0,1,…,q}, Under the saturated controller in step 2, the communication network control system in step 1 is positive and has stability with L1 gain performance; the saturated control gain matrix K i,s and the auxiliary gain matrix H i,s The specific form of the design is And the residence time method selects the minimum residence time method, and the switching condition meets: Among them, K i,s =[K i1,s K i2,s ], H i,s =[H i1,s H i2,s ], e q represents an r-dimensional column vector whose elements are all 1, represents an r-dimensional column vector whose mth element is 1 and the rest of the elements are 0. The symbol T represents the transpose of a vector or matrix; Step 4: The positive verification process of the communication network saturation control system is as follows: Consider the positivity of the continuous-time subsystem: Using the continuous-time subsystem saturation controller in step 2, we can obtain because and therefore Using formulas (3) and (4) in step 3, we have Combined with the continuous-time controller gain matrix K in step 3 i,s The specific form of Therefore, A i +B i K i is a Metzler matrix; since For any non-negative initial condition, the continuous-time subsystem in step 1 is positive; Step 5: The verification process of the stability of the communication network saturation control system is as follows: Step 5.1, select the linear cosine Lyapunov function as V(x(t))=x T (t)E T v σ(t) (t) (26) in, Based on the minimum residence time [t l ,t l+1 ) is divided into and In [t l , tl+1 ) Time period design definition Then v i (t) can be expressed as: At the same time, you can get in Step 5.2: First, consider When D iz and Three different situations; Step 5.2.

1. Case 1: When D iz ≠I, According to (5) and (8) in step 3, we can conclude that: Step 5.2.2, Case 2: When D iz =I, According to (6) and (9) in step 3, we can conclude that: Step 5.2.3, Case 3: When D iz =0, According to (7) and (10) in step 3, we can conclude that: Step 5.

3. Next, consider When D iz and Three different situations; Step 5.3.

1. Case 1: When D iz ≠I, According to (11) in step 3, we can conclude that: Step 5.3.2, Case 2: When D iz =I, According to (12) in step 3, we can conclude that: Step 5.3.3, Case 3: When D iz =0, According to step 3 (13), we can get: Step 5.

4. Therefore, combining formula (29) in step 5.2 and formula (30) in step 5.3, we can conclude that: Step 5.5: Through step 5.4, we can conclude: The following equation is obtained by using the Lyapunov function in step 5.1: When t∈[t l-1 ,t l ), σ(t)=j, when t∈[t l ,t l+1 ), σ(t)=i; Through step 3 (14), we can get: Step 5.6, finally we can conclude: Therefore, the communication network saturation control system has L1 gain stability.

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