CN118350193A - Method for designing set member filter based on incomplete measurement information - Google Patents

Abstract

The present application relates to the field of set membership filtering technology, and discloses a set membership filter design method based on incomplete measurement information in a complex network, which includes the following method steps: step one: establish a complex network system model; step two: control the noise in the system within the ellipsoid set; step three: control the nonlinear function in the system within the condition of sector boundedness; step four: introduce the measurement output of the RR protocol scheduling system; step five: establish a model to describe the incomplete measurement; step six: design a set membership filter based on incomplete measurement; step seven: solve the set membership filtering problem of the complex network system with incomplete measurement under the RR protocol; step eight: use numerical examples to prove the feasibility of the proposed filtering scheme. By establishing a complex network model to reflect the incomplete measurement information, a distributed filtering problem of a type of discrete nonlinear complex network with network bandwidth limitations is solved.

Description

A method for designing set-membership filters based on incomplete measurement information

Technical Field

The invention relates to the technical field of set membership filtering, and in particular to a set membership filter design method based on incomplete measurement information.

Background technique

In the past few decades, complex networks have attracted great attention due to their wide applications in various real-world systems. Unlike isolated nodes, the state estimation of each node in a complex network is determined not only by itself but also by its neighbors. Therefore, traditional isolated node filtering cannot be directly applied to complex networks. To solve this problem, various state estimation strategies for complex networks have been proposed, such as distributed ∞ filtering, extended Kalman filtering, and ensemble filtering. At the same time, a recursive state estimator has also been proposed, in which the gain matrix of each node is determined by optimizing the upper bound matrix.

Among the above methods, many filtering schemes have been developed, most of which require the system noise, including process noise and measurement noise, under a random framework, such as Kalman filtering. These filtering schemes not only lead to requirements on the mean and variance of the noise, but also cannot guarantee that the state is included in the region.

To overcome these difficulties, set membership estimation methods are currently proposed, which provide a set of state estimates containing the assumed unknown but bounded noise of the true state of the system, rather than a random description. On the other hand, it has been recognized that the application of set membership filtering is more convenient than Kalman filtering.

Therefore, the present invention aims to provide a set membership filter design method based on incomplete measurement information to improve the uncertainty problem in the system model.

Summary of the invention

In view of the shortcomings of the prior art, the present invention provides a set membership filter design method based on incomplete measurement information, aiming to solve the distributed filtering problem of a class of discrete nonlinear complex networks with network bandwidth limitations.

To achieve the above objectives, the present invention is implemented by the following technical solutions: a set membership filter design method based on incomplete measurement information in a complex network, comprising the following method steps:

Step 1: Establish a complex network system model;

Step 2: Control the noise in the system within the ellipsoid set;

Step 3: Control the nonlinear functions in the system within the condition of sector-boundedness;

Step 4: Introduce the measurement output of the RR protocol scheduling system;

Step 5: Build a model to describe incomplete measurement;

Step 6: Design a set membership filter based on incomplete measurement;

Step 7: Solve the membership filtering problem of complex network systems with incomplete measurements under the RR protocol;

Step 8: Use numerical examples to prove the feasibility of the proposed filtering scheme.

Preferably, the complex network system model in step 1 is:

_yi,k ＝Ci _{,kxi ,k} +Di _{, kvi,k}

where i and k represent the node and time respectively, _xi,k is the state of the system, _yi,k is the measured output of the system, f(·) is a known nonlinear function, Γ is the internal coupling matrix, _ωij is the external coupling matrix, _wi,k is the process noise, _vi,k is the measurement noise, and Ai _,K , Bi _,K , _Ci,k , Di _,k are known dimensionally appropriate matrices.

Preferably, in step 2, the noise is controlled within the ellipsoid set as follows:

Among them, _Si , _Ri are known appropriately dimensioned positive definite matrices.

Preferably, the step three controls the nonlinear function in the system within the condition of sector-boundedness:

[ _fi (x) _-fi (y) _-U1 (xy)] ^Τ [ _fi (x) _-fi (y) _-U2 (xy)]≤0

Among them, the nonlinear function _fi (·) is continuous and satisfies _fi (0) = 0, and U ₁ and U ₂ are known matrices of appropriate dimension.

Preferably, the measurement output of the RR protocol scheduling system introduced in step 4 is:

in, δ(·) is the Kronecker-δ function. When kl＜0, θ _kl ＝l; when k≤0, y _k ＝y ₀ , where y ₀ is the initial measured value.

Preferably, the measurement output of the RR protocol scheduling system needs to introduce a variable θ _i,k , _which is defined as:

Wherein, θ _i,k ∈{1,2,···,m}, according to the periodicity of the RR protocol, θ _k+m ＝θ _k .

Preferably, in step 5, a model is established to describe the incomplete measurement as follows:

Where _yi,k is the information actually received, Π _k = diag{π _1,k ,π _2,k ,···,π _m,k }, π _i,k ∈[π _i ,π _i ], 0≤π _i ≤π _i ≤1, i = 1, 2,···, m; let

in,

Preferably, in step 6, a set membership filter based on incomplete measurement is designed:

where _xi,k is the estimated value of xi _,k and _Lk is the set membership filter gain matrix.

Preferably, the step 7 solves the set membership filtering problem of the complex network system with incomplete measurement under the RR protocol:

For a given set of matrices P _k+1 > 0, it is guaranteed that the filtering error e _k+1 = x _k+1 - x _k+1 can satisfy:

Select a suitable gain matrix L _K to minimize the trace of the matrix P _k+1 .

The present invention provides a method for designing a set membership filter based on incomplete measurement information. It has the following beneficial effects:

1. The present invention reduces the network transmission burden by using a polling protocol. For the mutually independent random variables existing in the system matrix function, it is assumed that they obey a uniform distribution within a known finite range, and the process noise and measurement noise are unknown, bounded, and restricted to a specified ellipsoid set. By converting to inequality constraint processing, all allowable unknown but bounded noises, known deterministic inputs and incomplete measurements, the ellipsoid set, including all possible states, can be determined by a convex optimization method with probabilistic constraints, which has the advantages of simple periodicity and easy operation.

2. Based on the fact that the measurement output collected by sensors may be incomplete due to intermittent failures, structural mutations, aging and network noise in engineering practice, the present invention establishes a model to reflect the incomplete measurement, which has certain reliability and practicality and solves the distributed filtering problem of a class of discrete nonlinear complex networks with network bandwidth limitations.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of the method of the present invention;

FIG. 2 is a schematic diagram of a numerical example system simulation of the present invention.

Detailed ways

The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Example:

Referring to Figures 1 and 2, an embodiment of the present invention provides a method for designing a set membership filter based on incomplete measurement information in a complex network, comprising the following steps:

Step 1: Establish a complex network system model;

Step 2: Control the noise in the system within the ellipsoid set;

Step 3: Control the nonlinear functions in the system within the condition of sector-boundedness;

Step 4: Introduce the measurement output of the RR protocol scheduling system;

Step 5: Build a model to describe incomplete measurement;

Step 6: Design a set membership filter based on incomplete measurement;

Step 7: Solve the membership filtering problem of complex network systems with incomplete measurements under the RR protocol;

Step 8: Use numerical examples to prove the feasibility of the proposed filtering scheme;

Furthermore, the complex network system model in step 1 is:

_yi,k ＝Ci _{,kxi ,k} +Di _{, kvi,k}

Among them, i and k represent the node and time respectively, _xi,k is the state of the system, yi _,k is the measured output of the system, f() is a known nonlinear function, Γ is the internal coupling matrix, _ωij is the external coupling matrix, _wi,k is the process noise, _vi,k is the measurement noise, _Ai,K , _Bi,K , _Ci,k , _Di,k are known dimensionally appropriate matrices.

Furthermore, in step 2, the noise is controlled within the ellipsoid set as follows:

Among them, _Si , _Ri are known appropriately dimensioned positive definite matrices.

Furthermore, step three controls the nonlinear function in the system within the condition of sector-boundedness:

[ _fi (x) _-fi (y) _-U1 (xy)] ^Τ [ _fi (x) _-fi (y) _-U2 (xy)]≤0

Among them, the nonlinear function _fi (·) is continuous and satisfies _fi (0) = 0, and U ₁ and U ₂ are known dimensionally appropriate matrices:

Furthermore, the measurement output of the RR protocol scheduling system introduced in step 4 is:

in, δ(·) is the Kronecker-δ function. When kl＜0, θ _kl ＝l; when k≤0, y _k ＝y ₀ , where y ₀ is the initial measured value.

The measurement output of the RR protocol scheduling system is introduced, which is characterized in that: considering the measurement output of the RR protocol scheduling system, it is necessary to introduce a variable θ _i,k , _which can be defined as:

Wherein, θ _i,k ∈{1,2,···,m}, according to the periodicity of the RR protocol, θ _k+m ＝θ _k .

Furthermore, the model described in step 5 is established to describe the incomplete measurement as follows:

Where _yi,k is the actual received information, Π _k = diag{π _1,k ,π _2,k ,···,π _m,k }, π _i,k ∈[π _i ,π _i ], 0≤π _i ≤π _i ≤1, i = 1, 2,···, m. Let

in,

Furthermore, in step 6, a set membership filter based on incomplete measurement is designed:

where _xi,k is the estimated value of xi _,k and _Lk is the set membership filter gain matrix.

Furthermore, in step 7, the set membership filtering problem of complex network systems with incomplete measurements under the RR protocol is solved:

definition:

For a given set of matrices P _k+1 > 0, it is guaranteed that the filtering error e _k+1 = x _k+1 - x _k+1 can satisfy:

Select a suitable gain matrix L _K to minimize the trace of the matrix P _k+1 .

Lemma 1 (Shur's Lemma) If there exist matrices S ₁ , S ₂ and S ₃ of suitable dimensions, then Equivalent to:

or

Lemma 2 (S process) Given its about The quadratic function (j＝0,1,…,p), If there exist real numbers ε ₁ ≥ 0, ε ₂ ≥ 0, …, ε _P ≥ 0, such that

Theorem 1 Given a set P _k ＞0, the filtering error e _k satisfies If there exists a matrix P _k+1 > 0, a filter gain matrix L _k and a real number ε _j > 0 (j = 1, 2, ..., 8) such that the following matrix inequality holds:

Specifically, in the above formula:

and G _k is the given matrix The factor matrix of , then considering that the filtering error e _k+1 can be constrained to be within the ellipsoid set There exists a vector Z _k , satisfying ||Z _k ||≤1, so that the following equation holds

x _k = x _k + G _k Z _k

Where: G _k is a given matrix The factor matrix of .

Next, we calculate the filtering error e _k+1 and define:

because therefore:

Redefine:

but:

e _k+1 =Ω _k η _k

in: Therefore, we can get:

The following inequality holds:

in:

Therefore, η _k can be expressed as:

According to the nonlinear function f(x) belonging to the sector [U ₁ ,U ₂ ], it can be deduced that:

[f(x _k )-f(x _k )-U ₁ (x _k -x _k )] ^Τ [f(x _k )-f(x _k )-U ₂ (x _k -x _k )]≤0Substituting x _k =x _k +G _k Z _k into the above formula, we can obtain:

Equivalent to:

in:

Applying Lemma 2, if there exists a real number ε _j > 0 (j = 1, 2, ..., 10), the following equation holds:

Then there is Also holds true.

Therefore, the formula can also be abbreviated as:

By Lemma 1, The sufficient condition for the establishment of holds. Therefore, if the matrix inequality If holds, the filtering error e _k+1 can be constrained to be within the ellipsoid set Based on mathematical induction, Established, proven.

Corollary 1: If there exists a positive definite matrix P _k+1 , a filter gain matrix L _k and a real ε _j > 0 (j = 1, 2, ..., 10), the following optimization problem has a solution:

Then the minimum ellipsoid set sequence can be obtained.

Furthermore, in step eight, numerical examples are used to prove the feasibility of the proposed filtering scheme. In this step, in order to prove the feasibility of the proposed filtering scheme, simulation and analysis by using numerical examples have the following advantages:

You can fully compare the signal characteristics before and after filtering: select a specific signal as input and simulate the signal characteristics before and after filtering. By comparing the waveform, spectrum and other relevant characteristics before and after filtering, you can show the impact of the filtering scheme on the signal;

Specifically, by using numerical examples, we can simulate input signals of different frequencies, amplitudes, and phases, and observe the responses of the filter to these signals. By analyzing the output signal after filtering, we can evaluate the suppression effect of the filter on different frequency components, thereby proving the effectiveness of the filtering scheme.

Furthermore, if there are multiple filtering schemes to choose from, the superiority of the selected filtering scheme can be demonstrated by comparing the filtering effects of different types of filters (such as low-pass filters, band-pass filters, etc.) under the same input signal through numerical simulation;

The application of numerical examples can also calculate various performance indicators of the filtered signal, such as signal-to-noise ratio, distortion level, phase delay, etc. These indicators can help quantify the advantages and disadvantages of the filtering scheme;

Therefore, step eight of the embodiment of the present invention uses numerical examples to verify and analyze the proposed filtering scheme, which can fully verify the feasibility and benefits of the scheme of the present invention and provide theoretical support and guidance for the practical application of the filtering scheme.

Specifically, in this embodiment, by using the polling protocol to reduce the network transmission burden, there are some benefits in reducing the network transmission burden and set membership filtering, including:

Polling protocols usually adopt active polling or passive polling to obtain data from sensor nodes on demand. Compared with traditional transmission methods, polling protocols can reduce unnecessary data transmission, thereby saving network bandwidth usage, which helps to reduce the network transmission burden, especially in large-scale sensor networks.

In the polling protocol, data is usually sent from sensor nodes to data aggregation nodes, which can centrally process and filter the received data. This centralized filtering method can effectively reduce the amount of data transmitted in the network, and at the same time, the computing power of the data aggregation node can be used to perform more complex data processing and filtering operations, thereby improving the efficiency and accuracy of data processing.

In the polling protocol, the sensor node can sleep in the non-working state and wake up and send data only when it is polled. This low-power working mode can save the energy consumption of the sensor node, extend the working life of the sensor network, and save energy consumption.

Furthermore, through the polling protocol, the data aggregation node can perform quality control and filtering operations on the received data, eliminate abnormal data or noise, and improve the accuracy and reliability of the data. This is very important for some application scenarios that require high data accuracy.

In general, the benefits of the polling protocol in reducing network transmission burden and centralized filtering are mainly reflected in saving network bandwidth, realizing centralized processing and filtering, saving energy consumption, and improving data quality control. These benefits make the polling protocol have important application value in large-scale sensor networks and application scenarios with high data quality requirements.

At the same time, based on the fact that the measurement output collected by the sensor may be incomplete due to intermittent failures, structural mutations, aging and network noise of the sensor in engineering practice, the embodiment of the present invention establishes a model to reflect the incomplete measurement, which has certain reliability and practicality and effectively solves the distributed filtering problem of a class of discrete nonlinear complex networks with network bandwidth limitations.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims (9)

1. The method for designing the set member filter based on the incomplete measurement information in the complex network is characterized by comprising the following steps of:

step one: establishing a complex network system model;

Step two: controlling noise in the system in an ellipsoidal set;

Step three: controlling a nonlinear function in the system in a fan-shaped bounded condition;

step four: introducing measurement output of an RR protocol scheduling system;

Step five: modeling to describe incomplete measurements;

Step six: designing a set member filter based on incomplete measurement;

Step seven: the problem of member collection filtering of a complex network system which is incompletely measured under the RR protocol is solved;

Step eight: the feasibility of the proposed filtering scheme was demonstrated using numerical examples.

2. The method for designing a set membership filter based on incomplete measurement information in a complex network according to claim 1, wherein the complex network system model in the step one is:

y_i,k＝C_i,kx_i,k+D_i,kv_i,k

Where i and k represent node and time, respectively, x _i,k is the state of the system, y _i,k is the measured output of the system, f (·) is a known nonlinear function, Γ is the internal coupling matrix, ω _ij is the external coupling matrix, w _i,k is the process noise, v _i,k is the measured noise, and a _i,K,B_i,K,C_i,k,D_i,k is a known dimensionality matrix.

3. The method for designing a set member filter based on incomplete measurement information in a complex network according to claim 1, wherein the noise control in the step two is as follows:

wherein S _i,R_i is a known fitting positive definite matrix.

4. The method for designing a set membership filter based on incomplete measurement information in a complex network according to claim 1, wherein said step three controls a nonlinear function in the system within a fan-shaped bounded condition:

[f_i(x)-f_i(y)-U₁(x-y)]^Τ[f_i(x)-f_i(y)-U₂(x-y)]≤0

wherein the nonlinear function f _i (·) is continuous, satisfying f _i(0)＝0,U₁,U₂ is a known fit matrix.

5. The method for designing a set membership filter based on incomplete measurement information in a complex network according to claim 1, wherein the measurement output of the RR protocol scheduling system introduced in the fourth step is:

Wherein, Delta (·) is a Kronecker-delta function, θ _k-l =l when k-l < 0; y _k＝y₀,y₀ is the initial measurement when k.ltoreq.0.

6. The method for designing a set-up filter based on incomplete measurement information in a complex network according to claim 5, wherein the measurement output of the RR protocol scheduling system, the required introduction variable θ _i,k,θ_i,k is defined as:

Wherein, theta _i,k epsilon {1,2, (ii) the method comprises the steps of (1), m }, θ _k+m＝θ_k according to the periodicity of the RR protocol.

7. The method for designing a set-top filter based on incomplete measurement information in a complex network according to claim 1, wherein in the fifth step, a model is built to describe the incomplete measurement as:

Wherein, For the information actually received, pi _k＝diag{π_1,k,π_2,k,···,π_m,k,Order the

Wherein,

8. The method for designing the set membership filter based on incomplete measurement information in the complex network according to claim 1, wherein the method comprises the following steps: in the sixth step, a set member filter based on incomplete measurement is designed:

Wherein, Is an estimate of x _i,k, and L _k is the set-membership filter gain matrix.

9. The method for designing the set membership filter based on incomplete measurement information in the complex network according to claim 1, wherein the method comprises the following steps: in the seventh step, the problem of member filtering of the complex network system which is incompletely measured under the RR protocol is solved:

for a given set of matrices P _k+1 > 0, the filtering error is guaranteed Can satisfy:

The appropriate gain matrix L _K is selected to minimize the trace of matrix P _k+1.