CN118101489A - State estimation method, system and storage medium of nonlinear networked system based on asynchronous coding and decoding mechanism - Google Patents

Abstract

The invention provides a state estimation method, a state estimation system and a state estimation storage medium of a nonlinear networked system based on an asynchronous coding and decoding mechanism, belongs to the field of network control, and aims to solve the problem that the estimation precision of a state estimator is affected by neglecting quantization errors of the coding and decoding mechanism and delay existing in the process of the existing method. The method comprises the following steps: establishing a nonlinear networked system dynamic model with variance constraint and containing an asynchronous coding and decoding mechanism; inputting the state estimation value of the moment j at the moment j+1And estimating an error covariance matrix upper bound Θ _j|j, generating 2n _x +1 Sigma points, where n _x is the dimension of the state vector; calculating a numerical jacobian matrix of the nonlinear function according to the generated Sigma points, and approximating the nonlinear networked system to a linearization system; calculating the statistical characteristics of the quantization error, and eliminating the error; and solving an estimator gain matrix to realize nonlinear networked system state estimation with variance constraint of an asynchronous coding and decoding mechanism.

Description

A state estimation method, system and storage medium for nonlinear networked systems based on asynchronous coding and decoding mechanism

Technical Field

The invention belongs to the field of network control and relates to a state estimation method, system and storage medium of a nonlinear networked system with an asynchronous encoding and decoding mechanism.

Background technique

Networked systems enable users to perform remote data transmission and interactive operations through wireless communication networks, greatly reducing network costs, wiring complexity, and maintenance difficulties. In recent years, the state problem of networked systems has been widely studied, and a large number of estimation algorithms have been proposed. On the other hand, with the rapid development of digital communications, wireless communication networks have been widely used due to their advantages such as strong operability and low power consumption. Although wireless communication networks have some advantages, there are still some limitations, the two most important of which are limited network bandwidth and increasingly serious network security issues. In order to improve bandwidth utilization and transmission security at the same time, the encoding and decoding mechanism has received increasing attention. The encoding and decoding mechanism mainly consists of two parts: encoder (quantizer) and decoder. The measurement output first generates a special codeword under the action of the encoder, and then transmits it to the decoder through the wireless communication network. Finally, the decoded output is sent to the estimator for state estimation. Obviously, only the compiled codeword is transmitted through the wireless communication network. The encoding and decoding mechanism has broad application prospects and unique advantages in data compression and communication security.

Due to the introduction of the encoding and decoding mechanism, quantization errors will inevitably occur. On the other hand, due to the limitation of hardware devices, both the encoding and decoding processes require a certain amount of time, which means that there is a certain delay in the encoding and decoding process. Ignoring the quantization error and the time required for encoding and decoding may reduce the estimation accuracy of the state estimator and even cause the system to diverge. Therefore, a state estimation method for nonlinear networked systems with asynchronous encoding and decoding mechanisms is urgently needed to solve the quantization error and delay problems of the encoding and decoding mechanisms.

Summary of the invention

The technical problem to be solved by the present invention is:

Existing methods ignore the quantization error of the encoding and decoding mechanism and the delay in the process, which affects the estimation accuracy of the state estimator.

The technical solution adopted by the present invention to solve the above technical problems is as follows:

The present invention provides a state estimation method for a nonlinear networked system based on an asynchronous coding and decoding mechanism, characterized in that it comprises the following steps:

Step 1: Establish a nonlinear networked system dynamic model with variance constraints and asynchronous encoding and decoding mechanism;

Step 2: Set the initial value of state estimation and the initial value of covariance matrix;

Step 3: Input the estimated state value at time j at time j+1 And the upper bound of the estimated error covariance matrix Θ _j|j , generate 2n _x +1 Sigma points, where n _x is the dimension of the state vector;

Step 4: Calculate the numerical Jacobian matrix of the nonlinear function according to the Sigma points generated in step 3, and approximate the nonlinear networked system to a linearized system;

Step 5: Under the asynchronous coding and decoding mechanism, calculate the statistical characteristics of the quantization error and eliminate the error; construct a recursive estimator based on coding and decoding, calculate the estimated value at time j+1 and the upper bound matrix of the estimated error covariance, solve the estimator gain matrix, and realize the state estimation of the nonlinear networked system with variance constraints under the asynchronous coding and decoding mechanism;

Step 6: Determine whether the j+1 value exceeds the total duration N. If not, execute steps 3 to 5 at the next moment. Otherwise, end.

Furthermore, the state space form of the nonlinear networked system dynamic model with variance constraints containing the asynchronous encoding and decoding mechanism described in step 1 is:

In the formula, represents the state vector of the networked system at time j, /> and P _0|0 represent the initial value and initial variance of the state,/> is the measured output of the system, w _j and v _j are Gaussian noises with zero mean and variance R _j >0 and Q _j >0, respectively, h(·) is a nonlinear function,/> and/> is a known matrix of suitable dimension.

Furthermore, in the nonlinear networked system dynamic model with variance constraints containing an asynchronous encoding and decoding mechanism described in step 1, the encoder is defined as:

Where _sj is the codeword that needs to be sent to the decoder through the wireless communication network at time j, d>0 is the time required for encoding, q(·) is a uniform quantizer, and _ηj is the scaling function;

The form of the quantizer q(·) with quantization level 2L+1 is:

Where ζ is the quantization interval; according to the definition of q(·), we get:

in is the quantization error;

The decoder is defined as:

Where _yj is the decoded output received by the remote state estimator, and the positive integer τ represents the time required for decoding.

Furthermore, in the step 3, in the nonlinear function of the nonlinear networked system, by state estimation The upper bound of its estimated error covariance Θ _j|j selects the sigma point/> Right now:

In the formula Yes/> The jth column of , κ is a scalar that determines the propagation of sigma points; n _x is the dimension of the state vector, m = 2n _x +1;

The sigma point is mapped by a nonlinear function as follows:

Furthermore, step 4 includes the following process:

According to the Sigma points generated in step 3, the numerical Jacobian matrix of the nonlinear function is calculated, and the weighted least squares algorithm is introduced to calculate the optimal linearization matrix:

in,

For/> The i-th row of ; where diag{…} represents a diagonal matrix;

according to Definition, remove the last column of _Hj matrix to get the reduced dimension linear matrix:

in is the numerical Jacobian matrix of the nonlinear function, approximating the nonlinear networked system as a linearized system:

Furthermore, the calculation method of the statistical characteristics of the quantization error _Dj in step 5 is:

in

where Tr{·} represents the trace of the matrix, E{·} represents the expectation, o(z _i,j-ε ) and O(z _i,j-ε ) are the probability density function and cumulative distribution function of z _i,j-ε , respectively. Yes/> is the i-th component of , and Qi _,j-ε is the i-th diagonal element of Qj _-ε .

Furthermore, the recursive estimator based on asynchronous encoding and decoding is constructed in step 5 as follows:

in and/> are the one-step predicted value and estimated value of state x _j at time j, respectively./> Represents the total time required for the encoding and decoding process, /> is the estimator gain.

Furthermore, the solution process of the estimator gain matrix is:

The prediction error and estimation error are defined as:

Given positive scalars α ₁ ,α ₂ ,α ₃ ,α ₄ ,α ₅ ,α ₆ and α ₇ , satisfying the initial conditions The solutions of the two recursive equation matrices Θ _j+1|j+1 are:

in

δ ₁ =1+α ₁ +α ₂ +α ₃ , δ ₃ =1+α ₆ ,

is the upper bound of the estimated error covariance matrix;

Furthermore, through formula (17), we can get:

In order to minimize the upper bound of the estimated error covariance matrix, the estimated gain is constructed according to the result of formula (18): for:

in When , the trace of the upper bound of the estimated error covariance matrix can be minimized, where I represents the identity matrix.

A state estimation system for a nonlinear networked system based on an asynchronous coding and decoding mechanism, the system having a program module corresponding to the steps of any one of the above technical solutions, and executing the steps of the state estimation method for a nonlinear networked system based on an asynchronous coding and decoding mechanism during operation.

A computer-readable storage medium stores a computer program, wherein the computer program is configured to implement the steps of the state estimation method of a nonlinear networked system based on a coding and decoding mechanism described in any one of the above technical solutions when called by a processor.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention proposes a state estimation method, system and storage medium for a nonlinear networked system based on an asynchronous coding and decoding mechanism, introduces a linear fitting algorithm to linearize and approximate a nonlinear function, uses a coding and decoding mechanism to encrypt and compress the measurement data, and considers the delay problem that occurs during the coding and decoding process, and accurately calculates the variance characteristics of the quantization error caused by the coding and decoding mechanism. The constructed recursive state estimator can guarantee the performance index of the minimum estimation error covariance. The estimation method of the present invention can better reflect the actual working mode of the coding and decoding mechanism, and the estimation accuracy is higher. The analysis method is convenient to solve and easy to implement.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a state estimation method for a nonlinear networked system based on a coding and decoding mechanism according to an embodiment of the present invention;

FIG2 is a state change curve x1 _,j and _x2,j of a nonlinear network system in an embodiment of the present invention;

FIG3 is an upper bound curve of the estimation error covariance matrix in an embodiment of the present invention;

FIG4 is an estimation error curve according to an embodiment of the present invention;

FIG. 5 is a graph showing actual measurement output and codewords transmitted in a wireless communication network according to an embodiment of the present invention.

Detailed ways

In the description of the present invention, it should be noted that the terms "first", "second", and "third" mentioned in the embodiments of the present invention are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second", and "third" may explicitly or implicitly include one or more of the features.

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

Specific implementation scheme 1: In conjunction with FIG1 , the present invention provides a state estimation method for a nonlinear networked system based on an asynchronous encoding and decoding mechanism, comprising the following steps:

Step 1: Establish a nonlinear networked system dynamic model with variance constraints and asynchronous encoding and decoding mechanism;

Step 2: Set the initial value of state estimation and the initial value of covariance matrix;

Step 3: Input the estimated state value at time j at time j+1 And the upper bound of the estimated error covariance matrix Θ _j|j , generate 2n _x +1 Sigma points, where nx is the dimension of the state vector;

Step 4: Calculate the numerical Jacobian matrix of the nonlinear function according to the Sigma points generated in step 3, and approximate the nonlinear networked system to a linearized system;

Step 5: Under the asynchronous coding and decoding mechanism, calculate the statistical characteristics of the quantization error and eliminate the error; construct a recursive estimator based on coding and decoding, calculate the estimated value at time j+1 and the upper bound matrix of the estimated error covariance, solve the estimator gain matrix, and realize the state estimation of the nonlinear networked system with variance constraints under the asynchronous coding and decoding mechanism;

Step 6: Determine whether the j+1 value exceeds the total duration N. If not, execute steps 3 to 5 at the next moment. Otherwise, end.

Specific implementation scheme 2: The state space form of the nonlinear networked system dynamic model with variance constraints containing the asynchronous encoding and decoding mechanism described in step 1 is:

In the formula, represents the state vector of the networked system at time j, /> and P _0|0 represent the initial value and initial variance of the state,/> is the measured output of the system, w _j and v _j are Gaussian noises with zero mean and variance R _j >0 and Q _j >0, respectively, h(·) is a nonlinear function,/> and/> is a known suitable-dimensional matrix. The rest of this embodiment is the same as the first embodiment.

Specific implementation scheme three: The nonlinear networked system dynamic model with variance constraints containing an asynchronous encoding and decoding mechanism described in step one defines the encoder as:

Where _sj is the codeword that needs to be sent to the decoder through the wireless communication network at time j, d>0 is the time required for encoding, q(·) is a uniform quantizer, and _ηj is the scaling function;

The form of the quantizer q(·) with quantization level 2L+1 is:

Where ζ is the quantization interval; according to the definition of q(·), we get:

in is the quantization error;

The decoder is defined as:

Where _yj is the decoded output received by the remote state estimator, and the positive integer τ represents the time required for decoding. The rest of this implementation is the same as the second implementation.

Specific implementation scheme 4: In the step 3, in the nonlinear function of the nonlinear networked system, by state estimation The upper bound of its estimated error covariance Θ _j|j selects the sigma point/> Right now:

In the formula Yes/> The jth column of , κ is a scalar that determines the propagation of sigma points; n _x is the dimension of the state vector, m = 2n _x +1;

The sigma point is mapped by a nonlinear function as follows:

The rest of this embodiment is the same as the first specific embodiment.

Specific implementation plan five: Step four includes the following process:

According to the Sigma points generated in step 3, the numerical Jacobian matrix of the nonlinear function is calculated, and the weighted least squares algorithm is introduced to calculate the optimal linearization matrix:

in,

For/> The i-th row of ; where diag{…} represents a diagonal matrix;

according to Definition, remove the last column of _Hj matrix to get the reduced dimension linear matrix:

in is the numerical Jacobian matrix of the nonlinear function, approximating the nonlinear networked system as a linearized system:

The rest of this embodiment is the same as the first specific embodiment.

Specific implementation scheme six: The calculation method of the statistical characteristics of the quantization error _Dj in step five is:

in

where Tr{·} represents the trace of the matrix, E{·} represents the expectation, o(z _i,j-ε ) and O(z _i,j-ε ) are the probability density function and cumulative distribution function of z _i,j-ε , respectively. Yes/> The i-th component of , Qi _,j-ε is the i-th diagonal element of Qj _-ε . The rest of this implementation is the same as the first implementation.

Specific implementation plan seven: The recursive estimator based on asynchronous encoding and decoding constructed in step five is:

in and/> are the one-step predicted value and estimated value of state x _j at time j, respectively./> Represents the total time required for the encoding and decoding process, /> The rest of this embodiment is the same as the sixth embodiment.

Specific implementation scheme eight: The solution process of the estimator gain matrix is:

The prediction error and estimation error are defined as:

Design a recursive estimator for nonlinear systems affected by encoding and decoding mechanisms, and ensure that the estimated error covariance has an upper bound;

In addition, the trace of the upper bound of the estimation error covariance is minimized by the designed estimator gain;

Given positive scalars α ₁ ,α ₂ ,α ₃ ,α ₄ ,α ₅ ,α ₆ and α ₇ , satisfying the initial conditions The solutions of the two recursive equation matrices Θ _j+1|j+1 are:

in

δ ₁ =1+α ₁ +α ₂ +α ₃ , δ ₃ =1+α ₆ ,

is the upper bound of the estimated error covariance matrix;

Furthermore, through formula (17), we can get:

In order to minimize the upper bound of the estimated error covariance matrix, the estimated gain is constructed according to the result of formula (18): for:

in When , the trace of the upper bound of the estimated error covariance matrix can be minimized, where I represents the identity matrix. The rest of this embodiment is the same as the specific embodiment seven.

Specific implementation scheme nine: A state estimation system for a nonlinear networked system based on an asynchronous coding and decoding mechanism, the system having a program module corresponding to the steps of any technical solution of the above-mentioned specific implementation schemes, and executing the steps in the above-mentioned state estimation method for a nonlinear networked system based on an asynchronous coding and decoding mechanism during operation.

Specific implementation scheme ten: A computer-readable storage medium, the computer-readable storage medium storing a computer program, the computer program being configured to implement the steps in the state estimation method for a nonlinear networked system based on an asynchronous coding and decoding mechanism described in any one of the above-mentioned specific implementation schemes when called by a processor.

Example 1

In order to prove the effect of the method of the present invention, simulation verification is carried out based on the method of the present invention.

The system parameters are selected as:

in

In addition, the initial value and initial variance of the state are x _0|0 = [-0.5 1] ^T and The remaining parameters are selected as R _j = 0.01, Q _j = 0.01, η _j = 0.08, ζ = 0.16, l = 12. The coding and decoding delay is divided into two cases, case 1: d = 1, τ = 1, case 2: d = 3, τ = 3. The root mean square error (MSE) is defined as: N=300 is the number of independent experiments.

The simulation results are shown in Figures 2 to 5. As can be seen from Figure 2, LFA is the linear fitting algorithm proposed by the present invention, and TEM is the traditional Taylor expansion method. It can be seen from the figure that the estimation method proposed by the present invention is superior to the traditional algorithm. In addition, under the condition of different encoding and decoding delays, the higher the delay, the greater the estimation error, which is consistent with the theoretical analysis. As can be seen from Figure 3, the estimation error covariance matrix has an upper bound; as can be seen from Figure 4, the estimation error curve satisfies the mean square exponential boundedness, and the method proposed by the present invention has much smaller error than the traditional estimation algorithm; as can be seen from Figure 5, the actual measurement output of the system is inconsistent with the data transmitted in the wireless channel, so the data can be kept confidential to a large extent to prevent attackers from stealing and misappropriating. In summary, for nonlinear networked systems considering asynchronous encoding and decoding mechanisms, the invented recursive state estimation method is effective and feasible.

The state estimation method of a nonlinear networked system based on an asynchronous coding and decoding mechanism provided by the present invention is introduced in detail above. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims (10)

1. The state estimation method of the nonlinear networked system based on the asynchronous coding and decoding mechanism is characterized by comprising the following steps of:

Step one, establishing a nonlinear networked system dynamic model with variance constraint and containing an asynchronous coding and decoding mechanism;

step two, setting a state estimation initial value and a covariance matrix initial value;

Step three, inputting the state estimation value of the moment j at the moment j+1 And estimating an error covariance matrix upper bound Θ _j|j, generating 2n _x +1 Sigma points, where n _x is the dimension of the state vector;

Step four, calculating a numerical jacobian matrix of the nonlinear function according to the Sigma points generated in the step three, and approximating the nonlinear networking system to be a linearization system;

Step five, under an asynchronous coding and decoding mechanism, calculating the statistical characteristics of quantization errors, and eliminating the errors; constructing a recursive estimator based on coding and decoding, calculating an estimated value at the moment j+1 and an estimated error covariance upper bound matrix, solving an estimator gain matrix, and realizing nonlinear networked system state estimation with variance constraint of an asynchronous coding and decoding mechanism;

and step six, judging whether the value of j+1 exceeds the total duration N, if not, executing the step three to the step five at the next moment, and otherwise, ending.

2. The method for estimating the state of a nonlinear networked system based on an asynchronous codec according to claim 1, wherein in the step one, the state space form of the nonlinear networked system dynamic model with variance constraint containing the asynchronous codec is:

In the method, in the process of the invention, Representing a state vector at a time of networked system j,/>And P _0|0 represents the initial value and initial variance of the state,/>For the measurement output of the system, w _j and v _j are Gaussian noise with zero mean and variance R _j >0 and Q _j >0, respectively, h (·) is a nonlinear function,/>And/>Is a known dimension-adaptive matrix.

3. The method for estimating the state of a nonlinear networked system based on an asynchronous codec according to claim 2, wherein in the step one, the nonlinear networked system dynamic model with variance constraint containing the asynchronous codec defines an encoder as:

Wherein s _j is a codeword to be transmitted to a decoder through a wireless communication network at time j, d >0 is a time required for encoding, q (·) is a uniform quantizer, η _j is a scaling function;

The form of the quantizer q (·) with a quantization level 2l+1 is:

Wherein ζ is the quantization interval; according to the definition of q (·) we get:

Wherein the method comprises the steps of Is quantization error;

the decoder is defined as:

where y _j is the decoded output received by the far-end state estimator and the positive integer τ represents the time required for decoding.

4. The method for estimating the state of a nonlinear networked system based on an asynchronous codec mechanism according to claim 1, wherein in said step three, the state is estimated by a nonlinear function of the nonlinear networked systemAnd its upper bound Θ _j|j of estimated error covariance selects sigma point/>Namely:

In the middle of Is/>Kappa is a scalar that determines sigma point propagation; n _x is the dimension of the state vector, m=2n _x +1;

The sigma points are mapped by a nonlinear function as:

5. The method for estimating the state of a nonlinear networked system based on an asynchronous codec mechanism according to claim 1, wherein the fourth step comprises the following steps:

According to the Sigma points generated in the step three, calculating a numerical jacobian matrix of the nonlinear function, and introducing a weighted least square algorithm to calculate an optimal linearization matrix:

Wherein,

For/>I-th row of (a); wherein diag { … } represents a diagonal matrix;

According to Removing the last column of the H _j matrix to obtain a dimension-reduced linear matrix:

Wherein the method comprises the steps of As a numerical jacobian of a nonlinear function, a nonlinear networked system is approximated as a linearization system:

6. The method for estimating the state of a nonlinear networked system based on an asynchronous codec mechanism according to claim 1, wherein the calculating method of the statistical characteristic of the quantization error D _j in the fifth step is as follows:

Wherein the method comprises the steps of

Where Tr {. Cndot. } represents the trace of the matrix, E {. Cndot. } represents the expectation, O (z _i,j-ε) and O (z _i,j-ε) are the probability density function and the cumulative distribution function of z _i,j-ε, respectively,Is/>Q _i,j-ε is the i-th diagonal element of Q _j-ε.

7. The method for estimating the state of a nonlinear networked system based on an asynchronous codec mechanism according to claim 6, wherein constructing a recursive estimator based on codec in step five is:

Wherein the method comprises the steps of And/>One-step predicted value and estimated value of state x _j at moment j, respectively,/>Representing the total time required for the encoding and decoding process,/>Is the estimator gain.

8. The method for estimating the state of the nonlinear networked system based on the asynchronous codec according to claim 7, wherein the solving process of the estimator gain matrix is:

Defining a prediction error and an estimation error as:

given the positive scalar α ₁,α₂,α₃,α₄,α₅,α₆ and α ₇, the initial conditions are satisfied Solution Θ _j+1|j+1 of the two recursive equation matrices:

Wherein the method comprises the steps of

An upper bound for the estimated error covariance matrix;

further, it is obtained by the formula (17):

To minimize the upper bound of the estimation error covariance matrix, an estimation gain is constructed according to the result of equation (18) The method comprises the following steps:

Wherein the method comprises the steps of The trace of the upper bound of the estimation error covariance matrix, where I represents the identity matrix, can be minimized.

9. A state estimation system for an asynchronous codec mechanism based nonlinear networking system, characterized in that the system has program modules corresponding to the steps of any of the preceding claims 1-8, and that the steps in the state estimation method for an asynchronous codec mechanism based nonlinear networking system are executed at run-time.

10. A computer readable storage medium, characterized in that it stores a computer program configured to implement the steps in the state estimation method of the asynchronous codec mechanism based nonlinear networking system of any one of claims 1 to 8 when called by a processor.