Large-scale coupling network distributed optimization estimation method with security defense mechanism
By designing a distributed optimization estimation method with security defense mechanism in a large-scale coupled network, the accuracy and reliability problems of network node state estimation in dynamic and variable environments are solved, and efficient and accurate state estimation under network attack conditions is achieved.
Patent Information
- Application Number
- CN202411994342.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-31
- Publication Date
- 2025-05-13
AI Technical Summary
The prior art is difficult to efficiently and accurately estimate the status of multiple network nodes in a dynamic and changeable environment, especially when facing network attacks, which cannot effectively guarantee the integrity and reliability of data, which affects the estimation accuracy.
A large-scale distributed optimization estimation method for coupled networks with security defense mechanisms was designed. By establishing a discrete nonlinear stochastic dynamic model, considering linear false data injection attacks, designing decision functions to judge in real time that measurement data is attacked, identify and discard unreliable data, and design compensation strategies for discarded measurement information.
Large-scale coupled network node state estimation under uncertain coupling strength and linear false data injection attacks is realized, estimation accuracy is improved, the system's robustness and fault tolerance are ensured, adapt to dynamically changing environments, and real-time and efficient.
Smart Images
Figure CN119995937A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a large-scale coupled network distributed optimization estimation method with a safety defense mechanism, belonging to the technical field of state estimation. Background Art
[0002] Network node optimization estimation technology has been widely used in many fields such as navigation, traffic monitoring and military reconnaissance. However, the applicability of traditional single network node state estimation technology in practical engineering is often limited, and it cannot fully meet the state estimation needs of multi-coupled network nodes in complex environments. Therefore, the state estimation problem of multi-coupled network nodes has become an increasing research focus. How to efficiently and accurately estimate multiple network nodes in a dynamic and changing environment has become one of the core technical problems in this field. Solving this problem is not only of great significance to improving the accuracy and efficiency of related technologies, but also has broad prospects for promoting the development and application of modern science and technology. Therefore, in-depth research on large-scale coupled network state estimation methods will provide important support for scientific and technological innovation and technological progress.
[0003] In a networked environment, with the rapid development of information and communication technology, the openness and sharing of communication networks make data inevitably face the risk of network attacks during transmission. These attacks may cause the transmitted data to be tampered with or lost, thereby polluting the data transmitted to the estimator, which in turn seriously affects the estimation performance. When it comes to key applications such as large-scale coupled network node estimation, if an effective security defense mechanism is not designed to ensure the integrity and reliability of the data, its accuracy will be significantly affected, and may even lead to decision-making errors. Therefore, designing an estimation method with a security defense mechanism under network attacks is of great practical significance for the realization and optimization of large-scale coupled network node estimation technology.
[0004] The existing estimation methods cannot simultaneously handle the state estimation problem of large-scale coupled networks under uncertain coupling strength and linear false data injection attacks. If the traditional state estimation method is used to estimate the states of multiple network nodes, the estimation effect will be affected. Therefore, it is of practical significance to design a state estimation method that is applicable to these network-induced phenomena at the same time. Summary of the invention
[0005] In order to solve the problems existing in the background technology, the present invention provides a large-scale coupled network distributed optimization estimation method with a security defense mechanism.
[0006] To achieve the above object, the present invention adopts the following technical solution: a large-scale coupled network distributed optimization estimation method with a security defense mechanism, the method comprising the following steps:
[0007] S1: Establish discrete nonlinear stochastic dynamic models of large-scale coupled networks;
[0008] S101: Building discrete nonlinear stochastic dynamic models of large-scale coupled networks:
[0009]
[0010] In formula (1)-(2):
[0011] is the state vector of the i-th large-scale coupled network node at time t;
[0012] is the state vector of the jth large-scale coupled network node at time t;
[0013] i=1,2,…,N,j=1,2,…,N,i and j are the serial numbers of the large-scale coupled network nodes, and N represents the total number of large-scale coupled network nodes;
[0014] is the nonlinear function in the random dynamic model of large-scale coupled networks at time t;
[0015] is the state vector of the i-th large-scale coupled network node at time t+1;
[0016] ω ij,t is the coupling weight between the i-th large-scale coupled network node and the j-th large-scale coupled network node at time t, indicating that the state of each large-scale coupled network node will be affected by other network nodes;
[0017] Γ is the internal coupling matrix in the large-scale coupled network, indicating that the state vectors of each large-scale coupled network node will affect each other;
[0018] ζ i,t is the noise signal that describes the uncertain internal coupling situation in a large-scale coupled network, with a mean of zero and a variance of is a positive scalar τ i,t The square of
[0019] The system matrix for describing the uncertain internal coupling situation;
[0020] B i,t is the noise density matrix of the ith network node in the large-scale coupled network at time t;
[0021] is the process noise of the ith network node in the large-scale coupled network at time t, with a mean of zero and a variance of Q i,t ;
[0022] z i,t is the measured output of the ith network node at time t in the large-scale coupled network;
[0023] υ i,t is the measurement noise of the ith network node in the large-scale coupled network at time t, with a mean of zero and a variance of R i,t ;
[0024] S102: Considering a linear false data injection attack in a random form, the measurement model is constructed as follows:
[0025]
[0026] In formula (3):
[0027] is the actual measurement output of the i-th large-scale coupled network node at time t after being transmitted through the communication channel;
[0028] M i,t is a norm-bounded attack matrix that satisfies ||M i,t ||≤θ, θ is the attack matrix M i,t is the upper bound of the norm of , θ is a known positive scalar, ‖·‖ is the spectral norm of the matrix “·”;
[0029] ρ i,t is zero mean and has variance Λ i,t >0 noise signal;
[0030] λ i,t ∈{0,1} is a random variable that describes whether the measurement output of the i-th large-scale coupled network node at time t is attacked by linear false data injection, and has the following statistical characteristics:
[0031]
[0032] Where: Prob{·} is the probability of event “·” occurring, is the probability that the measurement output of the i-th network node is attacked by linear false data injection at time t;
[0033] S103: Design a decision function to determine in real time whether the received measurement data is under attack:
[0034]
[0035] In formula (4):
[0036] η i,t ∈{0,1} is the binary decision variable known to the i-th large-scale coupled network node at time t, if ηi,t =1, it means that the security defense mechanism believes that the measurement output of the i-th large-scale coupling network node at time t after being transmitted through the communication channel is Under attack, that is, the measurement is considered extremely unreliable and will not be used to update the estimate at the next moment;
[0037] is the decision function, where: is the intermediate variable, C i,t is the measurement matrix of the ith network node in the large-scale coupled network at time t, is the one-step prediction of the state of the i-th large-scale coupled network node at time t-1, l i,t is a known time-varying threshold; yes The transposed matrix of yes The transposed matrix of
[0038] S104: Design a compensation strategy for the discarded measurement information as follows:
[0039]
[0040] In formula (5):
[0041] is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t;
[0042] is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t-1.
[0043] S2: Design of time-varying recursive state estimators for discrete nonlinear stochastic dynamic models of large-scale coupled networks;
[0044] S201: Definition:
[0045] is the state vector With measurement output The augmented state variables;
[0046] is the augmented nonlinear function;
[0047] is the augmented noise density matrix;
[0048] is the augmented internal coupling matrix;
[0049] is the augmented system matrix describing the uncertain internal coupling situation;
[0050] is the augmented attack matrix;
[0051] To measure the noise i,t With the attack noise signal ρ i,t The augmented noise signal;
[0052]
[0053] Both are measured by the measurement matrix C i,t and the decision variable η i,t Different forms of system matrices are constructed; where: I is an identity matrix with appropriate dimensions; 0 is a zero matrix with appropriate dimensions;
[0054] S202: For the i-th network node in the large-scale coupled network, construct a two-step predictive state estimator:
[0055]
[0056] In formula (6)-(7):
[0057] is the next step prediction of the state of the i-th large-scale coupled network node at time t;
[0058] is the estimated form of the nonlinear function of the large-scale coupled network based on the i-th large-scale coupled network node at time t;
[0059] is the state estimation of the i-th large-scale coupled network node at time t;
[0060] is the state estimation of the jth large-scale coupled network node at time t;
[0061] The next step prediction of the state of the i-th large-scale coupled network node at time t+1;
[0062] S i,t+1 is the estimator parameter of the i-th large-scale coupled network node at time t+1;
[0063] is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t+1;
[0064] is the probability that the measurement output of the i-th large-scale coupled network node is attacked by linear false data injection at time t+1.
[0065] S3: Calculate the upper bound of the prediction error covariance of each large-scale coupled network node state;
[0066] The upper bound of the prediction error covariance of the node state in the large-scale coupled network described in S3 The calculation formula is as follows:
[0067]
[0068] In formula (8):
[0069] is the upper bound of the prediction error covariance of the i-th large-scale coupled network node state at time t;
[0070] is the upper bound of the estimated error covariance of the i-th large-scale coupled network node state at time t;
[0071] is the upper bound of the estimated error covariance of the j-th large-scale coupled network node state at time t;
[0072] A i,t is the nonlinear function corresponding to the state of the i-th large-scale coupled network node at time t In state estimation The Jacobian matrix at ;
[0073] Yes A i,t The transposed matrix of
[0074] yes The inverse matrix of
[0075] H i,t is a nonlinear function The known scaling matrix of the dependent system obtained based on the Taylor expansion formula;
[0076] E i,t is a nonlinear function A known adjustment matrix providing degrees of freedom obtained based on the Taylor expansion formula;
[0077] Yes H i,t The transposed matrix of
[0078] YesE i,t The transposed matrix of
[0079] β i,t is a known positive scalar that satisfies
[0080] β i,t The reciprocal of
[0081] yes The transposed matrix of
[0082] yes The transposed matrix of
[0083] yes The transposed matrix of
[0084] yes The transposed matrix of
[0085] yes The transposed matrix of
[0086] yes The transposed matrix of
[0087] yes The transposed matrix of
[0088] yes The transposed matrix of
[0089] The upper bound of the estimated error covariance is and state estimation The intermediate matrix formed;
[0090] is a matrix consisting of an identity matrix and a zero matrix of appropriate dimensions;
[0091] is the sum of the coupling weights of the i-th large-scale coupled network node at time t;
[0092] is the noise signal ζ that characterizes the uncertain internal coupling in large-scale coupled networks. i,t The variance of
[0093] Q i,t is the process noise of the ith network node in the large-scale coupled network at time t The variance of
[0094] The measured noise is i,t The variance R i,t and the attack noise signal ρ i,t The variance of i,t The noise variance matrix formed;
[0095] ∈1、∈2、∈3、∈4、∈5、∈6、∈7、∈8、∈9、∈ 10 and ∈ 11 are all known scaling parameters;
[0096] and are the scaling parameters ∈1, ∈2, ∈3, ∈4, ∈5, ∈6, ∈7, ∈8, ∈9, ∈ 10 and ∈ 11 The reciprocal of
[0097] yes The transposed matrix of
[0098] tr{·} means finding the trace of “·”.
[0099] S4: Design the estimator parameters of each large-scale coupled network node according to the upper bound of the prediction error covariance;
[0100] S4 is the estimator parameter S of the large-scale coupled network node i,t+1 The calculation formula is as follows:
[0101]
[0102] In formula (9):
[0103] ∈ 12 ,∈ 13 ,∈ 14 ,∈ 15 ,∈ 16 and ∈ 17 is a known scaling parameter;
[0104] and are the scaling parameters ∈ 12 ,∈ 13 ,∈ 14 ,∈ 15 ,∈ 16 and ∈ 17 The reciprocal of
[0105] The measured noise is i,t+1 The variance R i,t+1 and the attack noise signal ρ i,t+1 The variance of i,t+1 The noise variance matrix formed;
[0106] R i,t+1 is the measurement noise υ of the ith network node in the large-scale coupled network at time t+1 i,t+1 The variance of
[0107] The upper bound of the forecast error covariance is One-step prediction of the state The intermediate matrix formed;
[0108] yes The transposed matrix of
[0109] yes The transposed matrix of
[0110] yes The transposed matrix of
[0111] yes The transposed matrix of
[0112] yes The transposed matrix of
[0113] yes The inverse matrix of .
[0114] S5: Substitute the estimator parameters into the estimator, obtain the state estimation of the i-th large-scale coupled network node at time t+1, and determine whether the current time t+1 reaches the total time T. If t+1<T, execute S6; if t+1=T, end the estimation;
[0115] S6: Calculate the upper bound of the estimated error covariance of each large-scale coupled network node state according to the estimator parameters, set t=t+1, and execute S2 until t+1=T is satisfied.
[0116] The upper bound of the estimated error covariance of each node state in the large-scale coupled network described in S6 is The calculation process is as follows:
[0117] S601: Upper bound of the estimated error covariance of each node state in a large-scale coupled network The calculation formula is as follows:
[0118]
[0119] In formula (10):
[0120] YesS i,t+1 The transposed matrix of
[0121] S602: Make Established, of which: is the estimated error covariance of the i-th large-scale coupled network node at time t+1, is the estimation error of the i-th large-scale coupled network node at time t+1, To take the mathematical expectation of the random variable “·”, for The transposed matrix of
[0122] S603: By minimizing the upper bound of the estimation error covariance The trace of the estimator parameter S at time t+1 is obtained i,t+1 .
[0123] Compared with the prior art, the present invention has the following beneficial effects:
[0124] 1. The present invention simultaneously considers the impact of uncertain coupling strength and linear false data injection attacks on the network node state estimation performance. In particular, for the measurement data transmitted through the network, a corresponding security defense mechanism is designed at the end of the network transmission to determine in real time the situation in which the measurement data is attacked, identify and discard unreliable measurement data, and design a corresponding compensation strategy for the discarded measurement data.
[0125] 2. The present invention adopts a distributed state estimation method, which effectively improves the scalability and flexibility of the system by distributing the calculation and data processing tasks to multiple nodes, greatly reduces the communication burden, and avoids the single point failure problem that may occur in the centralized method. It not only improves the robustness and fault tolerance of the system, but also can adapt to dynamically changing environments, ensuring the real-time and high efficiency of multiple node estimation problems in large-scale coupled networks.
[0126] 3. The present invention solves the problem that the existing state estimation method cannot simultaneously handle the state estimation of large-scale coupled networks under uncertain coupling strength and linear false data injection attacks, thereby improving the estimation accuracy of such problems. It can be seen from the simulation diagram that as the probability of linear false data injection attacks increases, the mean square error also increases. When the attack probability changes from 0.35 to 0.55, the average mean square error increases by about 54.6%; when the attack probability changes from 0.55 to 0.75, the average mean square error increases by about 34.3%. This further verifies the feasibility and effectiveness of the state estimation method proposed in the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0127] Figure 1 is a flow chart of the present invention;
[0128] Figure 2 This is a comparison of the actual state trajectory and the estimated trajectory of the first Chua oscillator in a large-scale coupled network;
[0129] Figure 3This is a comparison of the actual state trajectory and the estimated trajectory of the second Chua oscillator in the large-scale coupled network;
[0130] Figure 4 This is a comparison of the actual state trajectory and the estimated trajectory of the third Chua oscillator in the large-scale coupled network;
[0131] Figure 5 This is a comparison of the actual state trajectory and the estimated trajectory of the fourth Chua oscillator in the large-scale coupled network;
[0132] Figure 6 is the logarithm of the mean square error of the state estimates of the first and second Chua oscillators in the large-scale coupled network (MSE i,t ) and the logarithm of the trace of the upper bound of the corresponding estimation error covariance Comparison chart of
[0133] Figure 7 is the logarithm of the mean square error of the state estimation of the third and fourth Chua oscillators in the large-scale coupled network (MSE i,t ) and the logarithm of the trace of the upper bound of the corresponding estimation error covariance Comparison chart of
[0134] Figure 8 is the measured output of the massively coupled Chua oscillator at different linear false data injection attack probabilities log(MSE t ) comparison chart. DETAILED DESCRIPTION
[0135] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0136] A large-scale coupled network distributed optimization estimation method with a security defense mechanism, the method comprising the following steps:
[0137] S1: Establish discrete nonlinear stochastic dynamic models of large-scale coupled networks;
[0138] S101: Building discrete nonlinear stochastic dynamic models of large-scale coupled networks:
[0139]
[0140] In formula (1)-(2):
[0141] is the state vector of the i-th large-scale coupled network node at time t;
[0142] is the state vector of the jth large-scale coupled network node at time t;
[0143] i=1,2,…,N,j=1,2,…,N,i and j are the serial numbers of the large-scale coupled network nodes, and N represents the total number of large-scale coupled network nodes;
[0144] is the nonlinear function in the random dynamic model of large-scale coupled networks at time t;
[0145] is the state vector of the i-th large-scale coupled network node at time t+1;
[0146] ω ij,t is the coupling weight between the i-th large-scale coupled network node and the j-th large-scale coupled network node at time t, indicating that the state of each large-scale coupled network node will be affected by other network nodes;
[0147] Γ is the internal coupling matrix in the large-scale coupled network, indicating that the state vectors of each large-scale coupled network node will affect each other;
[0148] ζ i,t is the noise signal that describes the uncertain internal coupling situation in a large-scale coupled network, with a mean of zero and a variance of is a positive scalar τ i,t The square of
[0149] The system matrix for describing the uncertain internal coupling situation;
[0150] B i,t is the noise density matrix of the ith network node in the large-scale coupled network at time t;
[0151] is the process noise of the ith network node in the large-scale coupled network at time t, with a mean of zero and a variance of Q i,t ;
[0152] z i,t is the measured output of the ith network node at time t in the large-scale coupled network;
[0153] υ i,t is the measurement noise of the ith network node in the large-scale coupled network at time t, with a mean of zero and a variance of R i,t ;
[0154] S102: Measurement data transmitted in a shared network environment may face the risk of false data injection attacks. Such attacks interfere with the authenticity and integrity of data by injecting forged or tampered false data, causing the receiver to obtain untrue information, which in turn affects system analysis, design, and decision-making. Considering a linear false data injection attack in a random form, the measurement model is constructed as follows:
[0155]
[0156] In formula (3):
[0157] is the actual measurement output of the i-th large-scale coupled network node at time t after being transmitted through the communication channel;
[0158] M i,t is a norm-bounded attack matrix that satisfies ||M i,t ||≤θ, θ is the attack matrix M i,t is the upper bound of the norm of , θ is a known positive scalar, ||·|| is the spectral norm of the matrix “·”;
[0159] ρ i,t is zero mean and has variance Λ i,t >0 noise signal;
[0160] λ i,t ∈{0,1} is a random variable that describes whether the measurement output of the i-th large-scale coupled network node at time t is attacked by linear false data injection, and has the following statistical characteristics:
[0161]
[0162] Where: Prob{·} is the probability of event “·” occurring, is the probability that the measurement output of the i-th network node is attacked by linear false data injection at time t;
[0163] S103: Since there are network attacks in the communication channel, in order to mitigate the impact and damage of network attacks on the estimation accuracy, a security defense mechanism is designed to identify and respond to potential network attacks in real time, thereby reducing the interference to the estimation process. A decision function is designed to determine in real time whether the received measurement data is under attack:
[0164]
[0165] In formula (4):
[0166] η i,t ∈{0,1} is the binary decision variable known to the i-th large-scale coupled network node at time t, if ηi,t =1, it means that the security defense mechanism believes that the measurement output of the i-th large-scale coupling network node at time t after being transmitted through the communication channel is It has been attacked with a high attack intensity, that is, the measurement value is considered extremely unreliable and will not be used to update the estimate at the next moment;
[0167] is the decision function, where: is the intermediate variable, C i,t is the measurement matrix of the ith network node in the large-scale coupled network at time t, is the one-step prediction of the state of the i-th large-scale coupled network node at time t-1, l i,t is a known time-varying threshold; yes The transposed matrix of yes The transposed matrix of
[0168] S104: Design a compensation strategy for the discarded measurement information as follows:
[0169]
[0170] In formula (5):
[0171] is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t;
[0172] is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t-1.
[0173] S2: Design of time-varying recursive state estimators for discrete nonlinear stochastic dynamic models of large-scale coupled networks;
[0174] S201: Definition:
[0175] is the state vector With measurement output The augmented state variables;
[0176] is the augmented nonlinear function;
[0177] is the augmented noise density matrix;
[0178] is the augmented internal coupling matrix;
[0179] is the augmented system matrix describing the uncertain internal coupling situation;
[0180] is the augmented attack matrix;
[0181] To measure the noise i,t With the attack noise signal ρ i,t The augmented noise signal;
[0182]
[0183] Both are measured by the measurement matrix C i,t and the decision variable η i,t Different forms of system matrices are constructed; where: I is an identity matrix with appropriate dimensions; 0 is a zero matrix with appropriate dimensions;
[0184] S202: For the i-th network node in the large-scale coupled network, construct a two-step predictive state estimator:
[0185]
[0186] In formula (6)-(7):
[0187] is the next step prediction of the state of the i-th large-scale coupled network node at time t;
[0188] is the estimated form of the nonlinear function of the large-scale coupled network based on the i-th large-scale coupled network node at time t;
[0189] is the state estimation of the i-th large-scale coupled network node at time t;
[0190] is the state estimation of the jth large-scale coupled network node at time t;
[0191] The next step prediction of the state of the i-th large-scale coupled network node at time t+1;
[0192] S i,t+1 is the estimator parameter of the i-th large-scale coupled network node at time t+1;
[0193] is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t+1;
[0194] is the probability that the measurement output of the i-th large-scale coupled network node is attacked by linear false data injection at time t+1.
[0195] S3: Calculate the upper bound of the prediction error covariance of each large-scale coupled network node state;
[0196] The upper bound of the prediction error covariance of the node state in the large-scale coupled network described in S3 The calculation formula is as follows:
[0197]
[0198] In formula (8):
[0199] is the upper bound of the prediction error covariance of the i-th large-scale coupled network node state at time t;
[0200] is the upper bound of the estimated error covariance of the state of the i-th large-scale coupled network node at time t;
[0201] is the upper bound of the estimated error covariance of the j-th large-scale coupled network node state at time t;
[0202] A i,t is the nonlinear function corresponding to the state of the i-th large-scale coupled network node at time t In state estimation The Jacobian matrix at ;
[0203] Yes A i,t The transposed matrix of
[0204] yes The inverse matrix of
[0205] H i,t is a nonlinear function The known scaling matrix of the dependent system obtained based on the Taylor expansion formula;
[0206] E i,t is a nonlinear function A known adjustment matrix providing degrees of freedom based on the Taylor expansion formula;
[0207] Yes H i,t The transposed matrix of
[0208] YesE i,t The transposed matrix of
[0209] β i,tis a known positive scalar that satisfies
[0210] β i,t The reciprocal of
[0211] yes The transposed matrix of
[0212] yes The transposed matrix of
[0213] yes The transposed matrix of
[0214] yes The transposed matrix of
[0215] yes The transposed matrix of
[0216] yes The transposed matrix of
[0217] yes The transposed matrix of
[0218] yes The transposed matrix of
[0219] The upper bound of the estimated error covariance is and state estimation The intermediate matrix formed;
[0220] is a matrix consisting of an identity matrix and a zero matrix of appropriate dimensions;
[0221] is the sum of the coupling weights of the i-th large-scale coupled network node at time t;
[0222] is the noise signal ζ that characterizes the uncertain internal coupling in large-scale coupled networks. i,t The variance of
[0223] Q i,t is the process noise of the ith network node in the large-scale coupled network at time t The variance of
[0224] The measured noise is i,t The variance Ri,t and the attack noise signal ρ i,t The variance of i,t The noise variance matrix formed;
[0225] ∈1、∈2、∈3、∈4、∈5、∈6、∈7、∈8、∈9、∈ 10 and ∈ 11 are all known scaling parameters;
[0226] and are the scaling parameters ∈1, ∈2, ∈3, ∈4, ∈5, ∈6, ∈7, ∈8, ∈9, ∈ 10 and ∈ 11 The reciprocal of
[0227] yes The transposed matrix of
[0228] tr{·} means finding the trace of “·”.
[0229] S4: Design the estimator parameters of each large-scale coupled network node according to the upper bound of the prediction error covariance;
[0230] S4 is the estimator parameter S of the large-scale coupled network node i,t+1 The calculation formula is as follows:
[0231]
[0232] In formula (9):
[0233] ∈ 12 ,∈ 13 ,∈ 14 ,∈ 15 ,∈ 16 and ∈ 17 is a known scaling parameter;
[0234] and are the scaling parameters ∈ 12 ,∈ 13 ,∈ 14 ,∈ 15 ,∈ 16 and ∈ 17 The reciprocal of
[0235] The measured noise is i,t+1 The variance R i,t+1 and the attack noise signal ρ i,t+1 The variance of i,t+1 The noise variance matrix formed;
[0236] Ri,t+1 is the measurement noise υ of the ith network node in the large-scale coupled network at time t+1 i,t+1 The variance of
[0237] The upper bound of the forecast error covariance is One-step prediction of the state The intermediate matrix formed;
[0238] yes The transposed matrix of
[0239] yes The transposed matrix of
[0240] yes The transposed matrix of
[0241] yes The transposed matrix of
[0242] yes The transposed matrix of
[0243] yes The inverse matrix of .
[0244] S5: Substitute the estimator parameters into the estimator, obtain the state estimation of the i-th large-scale coupled network node at time t+1, and determine whether the current time t+1 reaches the total time T. If t+1<T, execute S6; if t+1=T, end the estimation;
[0245] S6: Calculate the upper bound of the estimated error covariance of each large-scale coupled network node state according to the estimator parameters, set t=t+1, and execute S2 until t+1=T is satisfied.
[0246] The upper bound of the estimated error covariance of each node state in the large-scale coupled network described in S6 is The calculation process is as follows:
[0247] S601: Upper bound of the estimated error covariance of each node state in a large-scale coupled network The calculation formula is as follows:
[0248]
[0249] In formula (10):
[0250] YesS i,t+1 The transposed matrix of .
[0251] S602: Since there are uncertain terms in the estimated error covariance, its true value cannot be obtained, so the upper bound of the estimated error covariance of each large-scale coupled network node state is calculated. make Established, of which: is the estimated error covariance of the i-th large-scale coupled network node at time t+1, is the estimation error of the i-th large-scale coupled network node at time t+1, To take the mathematical expectation of the random variable “·”, for The transposed matrix of
[0252] S603: By minimizing the upper bound of the estimation error covariance The trace of the estimator parameter S at time t+1 is obtained i,t+1 .
[0253] Embodiment 1:
[0254] This embodiment takes the state estimation problem of a large-scale coupled Chua circuit consisting of four Chua oscillators as an example. They are connected through a coupling capacitor C c Mutual coupling. The coupling capacitor will transfer the output signal of oscillator 1 to oscillator 2, and the signal of oscillator 2 will also be fed back to oscillator 1 through the capacitor.
[0255] The present invention selects a large-scale coupled Chua circuit network consisting of four Chua oscillators for simulation. is the state of the i-th Chua oscillator at time t, where is the input signal of the oscillator, is the current, passing through the coupling capacitor C c Mutually coupled, here C c =ω ij,t The system parameters are as follows:
[0256] The noise density matrices are B 1,t =0.41I2, B 2,t =0.23I2,B 3,t =0.34I2 and B 4,t =0.43I2;
[0257] I2 is the two-dimensional identity matrix;
[0258] The internal coupling matrix is Γ = 0.15I2;
[0259] The system matrix describing the uncertain internal coupling situation is
[0260] Nonlinear functions The known scaling matrix H of the dependent system obtained based on Taylor expansion formula i,t =0.5I3, the known adjustment matrix E providing degrees of freedom obtained based on the Taylor expansion formula i,t =0.01I3;
[0261] I3 is the three-dimensional unit matrix;
[0262] The variance of the process noise is Q 1,t =Q 2,t =Q 3,t =Q 4,t =0.2I2;
[0263] The variance of the oscillator sensor measurement noise is R 1,t =R 2,t =R 3,t =R 4,t =0.1;
[0264] The variance of the Gaussian noise signal generated during the attack is Λ 1,t =Λ 2,t =Λ 3,t =Λ 4,t =0.1;
[0265] The linear false data injection attack probability is
[0266] The norm upper bound of the attack matrix is θ = 0.15;
[0267] The variance of the noise signal describing the uncertain internal coupling situation is
[0268] The judgment threshold in the security defense mechanism is l i,t =5.5sin(t);
[0269] The coupling weights between the four Chua oscillators are:
[0270] ω 24,t =ω 42,t =0.15;
[0271] ω 11,t =ω 13,t =ω 14,t =ω 31,t =ω 41,t =ω 44,t =0.2;
[0272] ω 12,t =ω 22,t =ω 33,t =ω 34,t =ω 21,t =ω 43,t =0.1;
[0273] ω 23,t =ω 32,t =0.3;
[0274] The measurement matrix of Chua's oscillator is:
[0275] C 1,t =[0.77+0.2sin(t)0.4];
[0276] C 2,t =[0.89+0.2sin(t)0.2];
[0277] C 3,t =[0.49+0.2sin(t)0.45];
[0278] C 4,t =[0.67+0.2sin(t)0.5];
[0279] The scaling parameters are ∈1=0.2, ∈2=8, ∈3=5, ∈4=10, ∈5=0.1, ∈6=0.1, ∈7=0.1, ∈8=0.1, ∈9=0.1, ∈ 10 =0.1,∈ 11 =0.1,∈ 12 =0.1,∈ 13 =0.1,∈ 14 =0.1,∈ 15 =0.1,∈ 16 =0.1 and∈ 17 =0.1;
[0280] The initial state vectors of the four Chua oscillators are [0.32-0.32] T , [-0.8-0.8] T , [0.24-0.16] T and [0.24-0.16] T ,T represents the transpose of the vector;
[0281] The initial state estimate of the estimator is the same as the initial state value of the oscillator; the initial value of the upper bound of the estimated error covariance of the four Chua oscillators is
[0282] The present invention uses mean square error to evaluate the algorithm performance, MSE i,t represents the mean square error of the i-th Chua oscillator at time t, and its calculation formula is:
[0283]
[0284] Where:
[0285] L = 10 is the number of Monte Carlo experiments;
[0286] and denote the actual state and estimated state of the i-th coupled Chua oscillator at time t in the r-th experiment, respectively;
[0287] for The transposed matrix of .
[0288] log(MSE t ) represents the logarithm of the mean square error of the state estimation of the four Chua oscillators at time t, that is, Where log(·) represents the logarithm of “·”. In particular, the mean square error is introduced to further measure the change of estimation performance under different linear false data injection attack probabilities, which is defined as In the present invention, T=90 is the total operation time.
[0289] Estimation effect of multiple coupled Chua oscillators:
[0290] Figure 2 , Figure 3 , Figure 4 and Figure 5 The attack probabilities are given as The actual state trajectory and estimated trajectory of the four coupled Chua oscillators when the linear false data injection attack is applied are shown in the figure. It can be seen from the figure that the estimation method with a security defense mechanism invented can effectively estimate the state of the large-scale coupled Chua circuit in real time for the large-scale coupled network under the influence of linear false data injection attack.
[0291] Figure 6 and Figure 7 The logarithm of the mean square error (MSE) of the state estimation of four coupled Chua oscillators is given respectively. i,t ) and the logarithm of the trace of the upper bound of the corresponding estimation error covariance From the comparison diagram, it can be seen that the trajectory of the mean square error is always lower than the trajectory of its upper bound. The experimental results verify the effectiveness of the estimation method proposed in this invention.
[0292] Figure 8 The log(MSE) of four coupled Chua's oscillators under different linear false data injection attack probabilities is given. t ), from which we can see that as the attack probability The increase in log(MSE t ) also increases, which shows that when When it increases, the estimation accuracy will be low. Furthermore, when the attack probability The average mean square error MSE′ of the state estimation of four coupled Chua oscillators when is 0.35, 0.55 and 0.75t They are approximately 1.322, 2.915 and 3.915 respectively. That is, when the attack probability changes from 0.35 to 0.55, the average mean square error increases by approximately 54.6%; when the attack probability changes from 0.55 to 0.75, the average mean square error increases by approximately 34.3%.
[0293] In summary, the distributed optimization estimation method for a large-scale coupled network with a security defense mechanism proposed in the present invention can also effectively estimate the real-time state of a large-scale coupled Chua's circuit under the influence of a linear false data injection attack.
[0294] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.
[0295] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.
Claims
1. A large-scale coupled network distributed optimization estimation method with a security defense mechanism, characterized by: The method comprises the following steps: S1: Establish discrete nonlinear stochastic dynamic models of large-scale coupled networks; S2: Design of time-varying recursive state estimators for discrete nonlinear stochastic dynamic models of large-scale coupled networks; S3: Calculate the upper bound of the prediction error covariance of each large-scale coupled network node state; S4: Design the estimator parameters of each large-scale coupled network node according to the upper bound of the prediction error covariance; S5: Substitute the estimator parameters into the estimator, obtain the state estimation of the i-th large-scale coupled network node at time t+1, and determine whether the current time t+1 reaches the total time T. If t+1<T, execute S6; if t+1=T, end the estimation; S6: Calculate the upper bound of the estimated error covariance of each large-scale coupled network node state according to the estimator parameters, set t=t+1, and execute S2 until t+1=T is satisfied.
2. According to claim 1, a large-scale coupled network distributed optimization estimation method with a security defense mechanism is characterized by: The S1 comprises the following steps: S101: Building discrete nonlinear stochastic dynamic models of large-scale coupled networks: In formula (1)-(2): is the state vector of the i-th large-scale coupled network node at time t; is the state vector of the jth large-scale coupled network node at time t; i=1,2,…,N,j=1,2,…,N,i and j are the serial numbers of the large-scale coupled network nodes, and N represents the total number of large-scale coupled network nodes; is the nonlinear function in the random dynamic model of large-scale coupled networks at time t; is the state vector of the i-th large-scale coupled network node at time t+1; ω ij,t is the coupling weight between the i-th large-scale coupled network node and the j-th large-scale coupled network node at time t, indicating that the state of each large-scale coupled network node will be affected by other network nodes; Γ is the internal coupling matrix in the large-scale coupled network, indicating that the state vectors of each large-scale coupled network node will affect each other; ζ i,t is the noise signal that describes the uncertain internal coupling situation in a large-scale coupled network, with a mean of zero and a variance of is a positive scalar τ i,t The square of The system matrix for describing the uncertain internal coupling situation; B i,t is the noise density matrix of the ith network node in the large-scale coupled network at time t; is the process noise of the ith network node in the large-scale coupled network at time t, with a mean of zero and a variance of Q i,t ; z i,t is the measured output of the ith network node at time t in the large-scale coupled network; υ i,t is the measurement noise of the ith network node in the large-scale coupled network at time t, with a mean of zero and a variance of R i,t ; S102: Considering a linear false data injection attack in a random form, the measurement model is constructed as follows: In formula (3): is the actual measurement output of the i-th large-scale coupled network node at time t after being transmitted through the communication channel; M i,t is a norm-bounded attack matrix that satisfies ||M i,t ||≤θ, θ is the attack matrix M i,t is the upper bound of the norm, θ is a known positive scalar, ‖·‖ is the spectral norm of the matrix "·"; ρ i,t is zero mean and has variance Λ i,t >0 noise signal; λ i,t ∈{0,1} is a random variable that describes whether the measurement output of the i-th large-scale coupled network node at time t is attacked by linear false data injection, and has the following statistical characteristics: Where: Prob{·} is the probability of event "·" occurring, is the probability that the measurement output of the i-th network node is attacked by linear false data injection at time t; S103: Design a decision function to determine in real time whether the received measurement data is under attack: In formula (4): η i,t ∈{0,1} is the binary decision variable known to the i-th large-scale coupled network node at time t, if η i,t =1, it means that the security defense mechanism believes that the measurement output of the i-th large-scale coupling network node at time t after being transmitted through the communication channel is the measurement value z i,t Under attack, that is, the measurement is considered extremely unreliable and will not be used to update the estimate at the next moment; is the decision function, where: is the intermediate variable, C i,t is the measurement matrix of the ith network node in the large-scale coupled network at time t, is the one-step prediction of the state of the i-th large-scale coupled network node at time t-1, l i,t is a known time-varying threshold; yes The transposed matrix of yes The transposed matrix of S104: Design a compensation strategy for the discarded measurement information as follows: In formula (5): is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t; is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t-1.
3. The method for distributed optimization estimation of a large-scale coupled network with a security defense mechanism according to claim 2, characterized in that: The S2 comprises the following steps: S201: Definition: is the state vector With measurement output The augmented state variables; is the augmented nonlinear function; is the augmented noise density matrix; is the augmented internal coupling matrix; is the augmented system matrix describing the uncertain internal coupling situation; is the augmented attack matrix; To measure the noise i,t With the attack noise signal ρ i,t The augmented noise signal; Both are measured by the measurement matrix C i,t and the decision variable η i,t Different forms of system matrices are constructed; where: I is an identity matrix with appropriate dimensions; 0 is a zero matrix with appropriate dimensions; S202: For the i-th network node in the large-scale coupled network, construct a two-step predictive state estimator: In formula (6)-(7): is the next step prediction of the state of the i-th large-scale coupled network node at time t; is the estimated form of the nonlinear function of the large-scale coupled network based on the i-th large-scale coupled network node at time t; is the state estimation of the i-th large-scale coupled network node at time t; is the state estimation of the jth large-scale coupled network node at time t; The next step prediction of the state of the i-th large-scale coupled network node at time t+1; S i,t+1 is the estimator parameter of the i-th large-scale coupled network node at time t+1; is the measurement output finally received by the estimator of the i-th large-scale coupled network node at time t+1; is the probability that the measurement output of the i-th large-scale coupled network node is attacked by linear false data injection at time t+1.
4. The method for distributed optimization estimation of a large-scale coupled network with a security defense mechanism according to claim 3 is characterized in that: The upper bound of the prediction error covariance of the node state in the large-scale coupled network described in S3 The calculation formula is as follows: In formula (8): is the upper bound of the prediction error covariance of the i-th large-scale coupled network node state at time t; is the upper bound of the estimated error covariance of the i-th large-scale coupled network node state at time t; is the upper bound of the estimated error covariance of the j-th large-scale coupled network node state at time t; A i,t is the nonlinear function corresponding to the state of the i-th large-scale coupled network node at time t In state estimation The Jacobian matrix at ; Yes A i,t The transposed matrix of yes The inverse matrix of H i,t is a nonlinear function The known scaling matrix of the dependent system obtained based on the Taylor expansion formula; E i,t is a nonlinear function A known adjustment matrix providing degrees of freedom obtained based on the Taylor expansion formula; Yes H i,t The transposed matrix of YesE i,t The transposed matrix of β i,t is a known positive scalar that satisfies β i,t The reciprocal of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of The upper bound of the estimated error covariance is and state estimation The intermediate matrix formed; is a matrix consisting of an identity matrix and a zero matrix of appropriate dimensions; is the sum of the coupling weights of the i-th large-scale coupled network node at time t; is the noise signal ζ that characterizes the uncertain internal coupling in large-scale coupled networks. i,t The variance of Q i,t is the process noise of the ith network node in the large-scale coupled network at time t The variance of The measured noise is i,t The variance R i,t and the attack noise signal ρ i,t The variance of i,t The noise variance matrix formed; ∈1、∈2、∈3、∈4、∈5、∈6、∈7、∈8、∈9、∈ 10 and ∈ 11 are all known scaling parameters; and are the scaling parameters ∈1, ∈2, ∈3, ∈4, ∈5, ∈6, ∈7, ∈8, ∈9, ∈ 10 and ∈ 11 The reciprocal of yes The transposed matrix of tr{·} means finding the trace of "·".
5. The method for distributed optimization estimation of a large-scale coupled network with a security defense mechanism according to claim 4 is characterized in that: S4 is the estimator parameter S of the large-scale coupled network node i,t+1 The calculation formula is as follows: In formula (9): ∈ 12 ,∈ 13 ,∈ 14 ,∈ 15 ,∈ 16 and ∈ 17 is a known scaling parameter; and are the scaling parameters ∈ 12 ,∈ 13 ,∈ 14 ,∈ 15 ,∈ 16 and ∈ 17 The reciprocal of The measured noise is i,t+1 The variance R i,t+1 and the attack noise signal ρ i,t+1 The variance of i,t+1 The noise variance matrix formed; R i,t+1 is the measurement noise υ of the ith network node in the large-scale coupled network at time t+1 i,t+1 The variance of The upper bound of the forecast error covariance is One-step prediction of the state The intermediate matrix formed; yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The transposed matrix of yes The inverse matrix of .
6. The method for distributed optimization estimation of a large-scale coupled network with a security defense mechanism according to claim 1, characterized in that: The upper bound of the estimated error covariance of each node state in the large-scale coupled network described in S6 is The calculation process is as follows: S601: Upper bound of the estimated error covariance of each node state in a large-scale coupled network The calculation formula is as follows: In formula (10): YesS i,t+1 The transposed matrix of S602: Make Established, of which: is the estimated error covariance of the i-th large-scale coupled network node at time t+1, is the estimation error of the i-th large-scale coupled network node at time t+1, To take the mathematical expectation of the random variable "·", for The transposed matrix of S603: By minimizing the upper bound of the estimation error covariance The trace of the estimator parameter S at time t+1 is obtained i,t+1 .