A state estimation method and system of a nonlinear networked system based on an asynchronous encoding-decoding mechanism and a storage medium

Abstract

The application provides a state estimation method and system of a nonlinear networked system based on an asynchronous encoding and decoding mechanism and a storage medium, and belongs to the network control field. The method is used for solving the problem that the existing method ignores the quantization error of the encoding and decoding mechanism and the delay existing in the process, and influences the estimation accuracy of the state estimator. The method comprises the following processes: a dynamic model of a nonlinear networked system with variance constraint and an asynchronous encoding and decoding mechanism is established; an upper bound Θ of a state estimation value and an estimation error covariance matrix at j time is input at j+1 time j|j , 2n x +1 Sigma points are generated, wherein n x is the dimension of a state vector; a numerical Jacobian matrix of a nonlinear function is calculated according to the generated Sigma points, the nonlinear networked system is approximated as a linearized system, the statistical characteristics of the quantization error are calculated, and the error is eliminated; and an estimator gain matrix is solved, so that the state estimation of the nonlinear networked system with variance constraint and the asynchronous encoding and decoding mechanism is realized.

Description

TECHNICAL FIELD

[0001] The application 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

[0002] The networked system enables users to remotely transmit data and interact through a wireless communication network, greatly reducing network cost, wiring complexity and maintenance difficulty. In recent years, the state problem of the networked system has been widely studied, and a large number of estimation algorithms have been proposed. On the other hand, with the rapid development of digital communication, wireless communication networks have been widely used due to their strong operability and low power consumption. Although wireless communication networks have some advantages, there are still some limitations, of which the two most important ones are limited network bandwidth and increasingly serious network security problems. In order to improve the bandwidth utilization and transmission security at the same time, the encoding and decoding mechanism has attracted more and more attention. The encoding and decoding mechanism mainly consists of an encoder (quantizer) and a decoder. The measurement output is first subjected to the action of the encoder to generate special code words, which are then transmitted to the decoder through the wireless communication network, and finally, the decoded output is sent to the estimator for state estimation. Obviously, only the encoded code words are transmitted through the wireless communication network, and the encoding and decoding mechanism has unique advantages in data compression and communication security.

[0003] Due to the introduction of the encoding and decoding mechanism, quantization errors will inevitably occur. On the other hand, the limitations of hardware devices result in a certain time required for the encoding and decoding processes, which means that there is a certain delay in the encoding and decoding processes. Ignoring the quantization errors and the time required for the encoding and decoding processes may reduce the estimation accuracy of the state estimator or even cause the system to diverge. Therefore, there is an urgent need for a state estimation method for a nonlinear networked system with an asynchronous encoding and decoding mechanism to solve the problems of quantization errors and delays in the encoding and decoding mechanism. SUMMARY

[0004] The technical problem solved by the present application is:

[0005] The existing method ignores the quantization errors and delays in the encoding and decoding mechanism, which affects the estimation accuracy of the state estimator.

[0006] The technical solution adopted by the present application to solve the above technical problem is:

[0007] The present application provides a state estimation method for a nonlinear networked system based on an asynchronous encoding and decoding mechanism, characterized by comprising the following steps:

[0008] Step one, establish a nonlinear networked system dynamic model with variance constraint containing an asynchronous encoding and decoding mechanism;

[0009] Step two, set the initial value of state estimation and covariance matrix initial value;

[0010] Step three, input the state estimation value at time and the upper bound of estimation error covariance matrix at time , generate Sigma points, where is the dimension of the state vector;

[0011] Step four, according to the Sigma points generated in step three, calculate the numerical Jacobian matrix of nonlinear function, and approximate the nonlinear networked system as a linearized system;

[0012] Step five, under the asynchronous encoding and decoding mechanism, calculate the statistical characteristics of quantization error, eliminate the error; construct the recursive estimator based on encoding and decoding, calculate the estimation value at time and the upper bound of estimation error covariance matrix, solve the estimator gain matrix, realize the state estimation of nonlinear networked system with variance constraint under the asynchronous encoding and decoding mechanism;

[0013] Step six, judge whether the value of exceeds the total duration N, if not, execute steps three to five at the next time, otherwise end.

[0014] Further, the dynamic model of nonlinear networked system with variance constraint containing asynchronous encoding and decoding mechanism in step one is in the form of state space as follows:

[0015] (1)

[0016] In the formula, represents the state vector of networked system at time , and and represent the initial value of state and initial variance, is the measurement output of the system, and are Gaussian noise with zero mean and variance and , respectively, is a nonlinear function, and are known square matrices.

[0017] Further, the dynamic model of nonlinear networked system with variance constraint containing asynchronous encoding and decoding mechanism in step one is defined as an encoder as follows:

[0018] ​​ (2)

[0019] in for The codewords that need to be sent to the decoder via a wireless communication network at any given time. The time required for encoding, It is a uniform quantizer. The scaling function;

[0020] Quantification level is Quantizer The form is:

[0021] (3)

[0022] in For quantization intervals; according to By definition, we get:

[0023] (4)

[0024] in This is for quantization error;

[0025] The decoder is defined as:

[0026] (5)

[0027] in The decoded output received by the remote state estimator, a positive integer. This represents the time required for decoding.

[0028] Furthermore, in step three, in the nonlinear function of the nonlinear networked system, state estimation is used... The upper bound of its estimation error covariance Choose sigma point ,Right now:

[0029] (6)

[0030] In the formula yes The List, For a scalar that propagates to a given sigma point; Let be the dimension of the state vector. ;

[0031] The sigma point is mapped to the following nonlinear function:

[0032] (7).

[0033] Furthermore, step four includes the following process:

[0034] Based on the Sigma points generated in step three, calculate the numerical Jacobian matrix of the nonlinear function, and then use a weighted least squares algorithm to calculate the optimal linearization matrix:

[0035] (8)

[0036] in,

[0037] (9)

[0038] for The ; among them, Represents a diagonal matrix;

[0039] according to Definition, removal The last column of the matrix yields a reduced-dimensional linear matrix:

[0040] (10)

[0041] in The numerical Jacobian matrix of the nonlinear function approximates the nonlinear network system as a linear system:

[0042] (11).

[0043] Furthermore, the quantization error in step five The method for calculating statistical characteristics is as follows:

[0044] (12)

[0045] in

[0046]

[0047]

[0048]

[0049] in Represents the trace of the matrix. Represents expectations, and They are respectively The probability density function and cumulative distribution function, yes The One portion, for The one diagonal element.

[0050] Further, the recursive estimator based on the asynchronous encoding-decoding in step five is constructed as:

[0051] (13)

[0052] where and are the one-step prediction and estimation of the state at time , respectively, denotes the total time required by the encoding-decoding process, is the estimator gain.

[0053] Further, the solution process of the estimator gain matrix is:

[0054] Define the prediction error and the estimation error as:

[0055] (14)

[0056] (15)

[0057] Given positive scalar and , satisfying the initial condition , the solution of the two recursive equation matrices is:

[0058] (16)

[0059] (17)

[0060] where

[0061]

[0062] is the upper bound of the estimation error covariance matrix;

[0063] Further, by formula (17), we have:

[0064] (18)

[0065] In order to minimize the upper bound of the estimation error covariance matrix, according to the results of formula (18), the estimation gain is constructed as:

[0066] (19)

[0067] where The trace of the upper bound of the estimation error covariance matrix can be minimized, where I represents a unit matrix.

[0068] A state estimation system of a nonlinear networked system based on an asynchronous encoding-decoding mechanism, the system has a program module corresponding to the steps of any of the above technical solutions, and when running, the steps in the state estimation method of the nonlinear networked system based on the encoding-decoding mechanism are executed.

[0069] A computer readable storage medium stores a computer program, the computer program is configured to be called by a processor to realize the steps in the state estimation method of the nonlinear networked system based on the encoding-decoding mechanism of any of the above technical solutions.

[0070] Compared with the prior art, the beneficial effects of the present application are:

[0071] The present application proposes a state estimation method, system and storage medium of a nonlinear networked system based on an asynchronous encoding-decoding mechanism, introduces a linear fitting algorithm to linearize and approximate a nonlinear function, uses an encoding-decoding mechanism to encrypt and compress measurement data, considers the delay problem in the encoding-decoding process, and accurately calculates the variance characteristics of the quantization error caused by the encoding-decoding mechanism. The constructed recursive state estimator can guarantee the performance index of the minimum estimation error covariance. The estimation method of the present application can better reflect the actual working mode of the encoding-decoding mechanism, and has higher estimation accuracy. The analysis method is convenient to solve and easy to implement. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 The state estimation method flowchart of the nonlinear networked system based on the encoding-decoding mechanism in the embodiment of the present application;

[0073] Figure 2 The state change curve of the nonlinear network system in the embodiment of the present application And ;

[0074] Figure 3 The upper bound curve of the estimation error covariance matrix in the embodiment of the present application;

[0075] Figure 4 The estimation error curve in the embodiment of the present application;

[0076] Figure 5 The actual measurement output and the code word curve transmitted in the wireless communication network in the embodiment of the present application. DETAILED DESCRIPTION

[0077] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0078] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0079] Specific Implementation Plan 1: Combining Figure 1 This invention provides a state estimation method for a nonlinear networked system based on an asynchronous encoding and decoding mechanism, comprising the following steps:

[0080] Step 1: Establish a dynamic model of a nonlinear networked system with variance constraints, incorporating an asynchronous encoding and decoding mechanism;

[0081] Step 2: Set the initial values ​​for the state estimate and the covariance matrix;

[0082] Step 3, in Input at any time State estimate at time 1 and the upper bound of the estimation error covariance matrix ,generate There are Sigma points, among which Let be the dimension of the state vector;

[0083] Step 4: Based on the Sigma points generated in Step 3, calculate the numerical Jacobian matrix of the nonlinear function to approximate the nonlinear network system as a linear system.

[0084] Step 5: Under the asynchronous encoding and decoding mechanism, calculate the statistical characteristics of the quantization error and eliminate the error; construct a recursive estimator based on encoding and decoding, and calculate... The estimated value at time and the upper bound matrix of the covariance of the estimation error are used to solve the estimator gain matrix, thereby realizing the state estimation of a nonlinear networked system with variance constraints using an asynchronous encoding and decoding mechanism.

[0085] Step Six: Judgment If the value exceeds the total duration N, then proceed to steps three through five at the next moment; otherwise, end the process.

[0086] Specific Implementation Plan Two: The dynamic model of the nonlinear networked system with variance constraints containing the asynchronous encoding and decoding mechanism described in Step One has the following state-space form:

[0087] (1)

[0088] wherein, represents a networked system state vector at time t, and represents the initial value of state and initial variance, is the measurement output of the system, and are Gaussian noises with zero mean and variance and respectively, is a nonlinear function, and are known square matrices. Other aspects of the present embodiment are the same as those of embodiment one.

[0089] Embodiment three: the nonlinear networked system dynamic model with variance constraint and the asynchronous encoder-decoder mechanism in step one, the encoder is defined as:

[0090] (2)

[0091] wherein is the codeword at time t that needs to be sent to the decoder through the wireless communication network, is the time needed for encoding, is a uniform quantizer, is a scaling function; The quantization level of the quantizer

[0092] is in the form of: (3)

[0093] wherein is the quantization interval; according to the definition of

[0094] , we have: (4)

[0095] wherein

[0096] is the quantization error;

[0097] The decoder is defined as:

[0098] (5)

[0099] wherein is the decoded output received by the remote state estimator, and the positive integer represents the time needed for decoding. Other aspects of the present embodiment are the same as those of embodiment two.​​

[0100] Specific embodiment four: in the nonlinear function of the nonlinear networked system in step three, the state estimation and its estimation error covariance upper bound Select sigma points That is:

[0101] (6)

[0102] In the formula is the first column of , a scalar that determines the propagation of sigma points; is the dimension of the state vector, ;

[0103] The sigma points are mapped to the nonlinear function as:

[0104] (7).

[0105] The other embodiments of this embodiment are the same as specific embodiment one.

[0106] Specific embodiment five: step four includes the following process:

[0107] According to the Sigma points generated in step three, the numerical Jacobian matrix of the nonlinear function is calculated, and the weighted least squares algorithm is introduced to calculate the optimal linearization matrix:

[0108] (8)

[0109] Where,

[0110] (9)

[0111] is the first row of ; Where, denotes a diagonal matrix;

[0112] According to the definition of , the last column of matrix is removed to obtain a reduced linear matrix:

[0113] (10)

[0114] Where is the numerical Jacobian matrix of the nonlinear function, and the nonlinear networked system is approximated as a linearized system:

[0115] (11).

[0116] The other parts of this embodiment are the same as embodiment one.

[0117] Embodiment six: quantization error in step five The calculation method of statistical properties is:

[0118] (12)

[0119] where

[0120]

[0121]

[0122]

[0123] where represents the trace of a matrix, represents the expectation, and are the probability density function and cumulative distribution function of , respectively, is the th component of , and is the th diagonal element of . The other parts of this embodiment are the same as embodiment one.

[0124] Embodiment seven: the recursive estimator based on asynchronous encoding-decoding in step five is:

[0125] (13)

[0126] where and are the one-step prediction and estimation of state at time , respectively, represents the total time required by the encoding-decoding process, is the estimator gain. The other parts of this embodiment are the same as embodiment six.

[0127] Embodiment eight: the solution process of the estimator gain matrix is:

[0128] Define the prediction error and estimation error as:

[0129] (14)

[0130] (15)

[0131] A recursive estimator is designed for a nonlinear system affected by an encoder-decoder mechanism, and an upper bound of the estimation error covariance is ensured;

[0132] Furthermore, the estimator gain is designed to minimize the trace of the upper bound of the estimation error covariance;

[0133] Given positive scalar and , the solution of the two recursive equation matrices satisfying the initial condition is :

[0134] (16)

[0135] (17)

[0136] where

[0137]

[0138] is an upper bound of the estimation error covariance matrix;

[0139] Further, from equation (17) we have

[0140] (18)

[0141] To minimize the upper bound of the estimation error covariance matrix, according to the result of equation (18), the estimation gain is constructed as

[0142] (19)

[0143] where , the trace of the upper bound of the estimation error covariance matrix is minimized, where I represents an identity matrix. Other aspects of this embodiment are the same as embodiment seven.

[0144] Embodiment nine: a state estimation system for a nonlinear networked system based on an asynchronous encoder-decoder mechanism, the system having program modules corresponding to the steps of any of the above technical solutions, and when running, performing the steps of the state estimation method for a nonlinear networked system based on an asynchronous encoder-decoder mechanism.

[0145] Embodiment ten: a computer readable storage medium storing a computer program, the computer program being configured to implement the steps of the state estimation method for a nonlinear networked system based on an asynchronous encoder-decoder mechanism when called by a processor.

[0146] Example 1

[0147] To demonstrate the effectiveness of the method of the present invention, simulation verification was performed based on the method of the present invention.

[0148] The system parameters are selected as follows:

[0149]

[0150] in

[0151]

[0152] Furthermore, the initial values ​​and initial variances of the state are respectively and The remaining parameters are selected as follows: , , Encoding and decoding latency can be divided into two cases, case one is: Scenario two is: The root mean square error (MSE) is defined as: , It represents the number of independent experiments.

[0153] Simulation effect as Figures 2 to 5 As shown, by Figure 2 As can be seen, LFA is the linear fitting algorithm proposed in this invention, while TEM is the traditional Taylor expansion method. The figure shows that the estimation method proposed in this invention is superior to traditional algorithms. Furthermore, with different encoding and decoding delays, the higher the delay, the greater the estimation error, which is consistent with theoretical analysis. Figure 3 It is evident that the estimated error covariance matrix has an upper bound; from Figure 4 It is evident that the estimation error curve satisfies the mean square exponential boundedness, and the method proposed in this invention has a significantly smaller error compared to traditional estimation algorithms; Figure 5 As can be seen, the actual measured output of the system is inconsistent with the data transmitted in the wireless channel, thus largely protecting the data and preventing attackers from stealing and misappropriating it. In summary, the invented recursive state estimation method is effective and feasible for nonlinear networked systems considering asynchronous encoding and decoding mechanisms.

[0154] The above provides a detailed description of the state estimation method for nonlinear networked systems based on asynchronous encoding and decoding mechanisms provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, those skilled in the art will recognize that there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for state estimation of a nonlinear networked system based on an asynchronous encoding-decoding mechanism, characterized in that, The method comprises the following steps: Step one, establishing a nonlinear networked system dynamic model with variance constraint containing an asynchronous encoding-decoding mechanism; Step two, setting initial values of state estimation and initial values of covariance matrix; Step three, at the time input the state estimate value and the estimation error covariance matrix upper bound , generate Sigma points, where is the dimension of the state vector; Step four, according to the Sigma points generated in step three, calculating the numerical Jacobian matrix of the nonlinear function, and approximating the nonlinear networked system as a linearized system; Step five, under the asynchronous encoding-decoding mechanism, the statistical properties of quantization error are calculated, and the error is eliminated; the recursive estimator based on encoding-decoding is constructed, and The estimation value and the estimation error covariance upper bound matrix of the time are calculated, the estimator gain matrix is solved, and the state estimation of the nonlinear networked system with variance constraint under the asynchronous encoding-decoding mechanism is realized. Step six, judging whether the value exceeds the total duration N, if not, executing steps three to five at the next time, otherwise ending; Step four comprises the following process: According to the Sigma points generated in step three, calculating the numerical Jacobian matrix of the nonlinear function, and introducing a weighted least square algorithm to calculate the optimal linearization matrix: （8） Wherein, （9） wherein, denotes a diagonal matrix, is the first row, is a scalar that determines the sigma point propagation; is the dimension of the state vector, ; According to the definition, removing the last column of the matrix results in a reduced-rank linear matrix: （10） wherein The numerical Jacobian matrix is a nonlinear function, and the nonlinear networked system is approximated as a linearized system: （11） wherein, is a known suitable matrix, represents a networked system state vector at time instant, is a Gaussian noise with zero mean and variance.

2. The state estimation method for nonlinear networked systems based on an asynchronous coding-decoding mechanism according to claim 1, characterized in that, The nonlinear networked system dynamic model with variance constraint containing an asynchronous encoding-decoding mechanism in step one has a state space form as follows: （1） In the formula, For the system's measurement output, It has zero mean and zero variance and Gaussian noise, It is a nonlinear function. Let be a known matrix of appropriate dimensions.

3. The method for state estimation of nonlinear networked systems based on an asynchronous encoding-decoding mechanism according to claim 2, characterized in that, The nonlinear networked system dynamic model with variance constraint containing an asynchronous encoding-decoding mechanism in step one defines the encoder as: （2） wherein is the codeword that needs to be transmitted over the wireless communication network to the decoder at the instant t, is the time needed for the encoding, is a uniform quantizer, is a scaling function; The quantization level is Quantizer In the form of: （3） wherein is the quantization interval; according to by definition, we get: （4） wherein is the quantization error; The decoder is defined as: （5） wherein decoded output received by the remote state estimator, positive integer represents the time required for decoding.

4. The method for state estimation of nonlinear networked systems based on an asynchronous encoding-decoding mechanism according to claim 1, characterized in that, In step three, in the nonlinear function of the nonlinear networked system, the state estimation and its upper bound of estimation error covariance selecting sigma points i.e.: （6） In the formulae is the first column; The Sigma points are mapped to the nonlinear function as follows: （7）。 5. The method for state estimation of nonlinear networked systems based on an asynchronous coding-decoding mechanism according to claim 1, characterized in that, Quantization error in step five The method for calculating the statistical properties is: （12） Wherein wherein denotes the trace of a matrix, denotes expectation, and are respectively the probability density function and the cumulative distribution function of is the th component of is the th diagonal element of denotes the total time needed for the encoding-decoding process.

6. The method for state estimation of nonlinear networked systems based on an asynchronous encoding-decoding mechanism according to claim 5, characterized in that, The recursive estimator based on encoding-decoding in step five is constructed as follows: （13） where and are respectively one-step prediction and estimation of the state at time is the estimator gain.​ 7. The method for state estimation of nonlinear networked systems based on an asynchronous encoding-decoding mechanism according to claim 6, characterized in that, The solving process of the estimator gain matrix is as follows: Define the prediction error and the estimation error as follows: （14） （15） Given positive scalar and satisfying the initial condition the solution of the two recursive equation matrices : （16） （17） Wherein is the upper bound of the estimation error covariance matrix; Further, it can be obtained from formula (17) as follows: （18） To minimize the upper bound of the estimation error covariance matrix, according to the result of (18), the estimation gain is constructed as is: （19） wherein At time t, the trace of the upper bound of the estimation error covariance matrix can be minimized, where I denotes the identity matrix.

8. A state estimation system for a nonlinear networked system based on an asynchronous encoding-decoding mechanism, characterized in that, The system has program modules corresponding to the steps of any one of the above claims 1-7, and when running, the steps of the state estimation method of the nonlinear networked system based on the asynchronous encoding-decoding mechanism are executed.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is configured to realize the steps of the state estimation method of the nonlinear networked system based on the asynchronous encoding-decoding mechanism in any one of claims 1-7 when called by the processor.

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