Privacy protection approximate average consensus method of networked system

Abstract

The invention discloses a privacy protection approximate average consensus method of a networked system. According to the method, a first mask and a second mask are randomly generated, and the requirements that the difference between the first mask and a common constant is absolutely summable, the second mask is absolutely summable, and the common constant is not zero are met; the product of the first mask and the current state is calculated, the product and the second mask are added to obtain the outward sending amount, and the outward sending amount is sent to the neighbor node; weighted summation is carried out on the received outward sending amount and the outward sending amount sent by the network system according to a preset weight, the preset weight of the weighted summation is larger than 0, the sum is 1, the weighted summation result is divided by the public constant, the updating amount is obtained, and a weight matrix of the network system is a symmetric matrix; weighted summation is carried out on the update quantity and the initial state value, an updated state value is obtained, the weight of weighted summation is a fixed value and is larger than 0, and the sum is 1. The method can realize approximate average consensus, and is high in privacy protection capability and low in operand.

Description

Technical Field

[0001] This invention relates to a privacy-preserving approximate average consensus method for networked systems, a networked system, and a program product. Background Technology

[0002] A networked system consists of a large number of nodes with autonomous decision-making, sensing, and communication capabilities coupled through a network topology. Each node relies solely on its neighbors for information exchange and local computation. In a networked system, each node has a state variable, which abstractly represents the node's characteristics. In specific applications, the state variable can correspond to position (coordinates, orientation, etc.), motion parameters (velocity, acceleration, angular velocity, angular acceleration, etc.), energy consumption, inventory levels, or other physical parameters, thus providing a basis for collaborative decision-making in the networked system. State values ​​can be scalars or vectors.

[0003] As a fundamental tool for distributed coordination and information fusion in networked systems, the average consensus algorithm plays an irreplaceable role in decentralized systems. It achieves consistent convergence of global information through local interactions, providing an efficient and scalable collaborative mechanism for networked systems. Therefore, the average consensus algorithm is widely used in tasks such as state estimation, resource allocation, load balancing, and group collaboration, playing a crucial role in supporting control decisions and optimization in networked systems.

[0004] The fundamental goal of average consensus in networked systems is to gradually converge the states of nodes through distributed iterations, without centrally aggregating state data, until the arithmetic mean of the initial states of the entire network is reached. A typical approach is to weight and fuse neighbor information based on a weight matrix corresponding to the topology. Convergence can be guaranteed when the nodes are undirected and the weights satisfy appropriate randomness conditions. Because of its characteristic of gradually unifying node states through local interactions, average consensus possesses good scalability and robustness, and has been widely applied in practical scenarios such as industrial internet information fusion, edge-side distributed optimization and collaborative decision-making, load balancing in computing and energy systems, and unmanned system formation consistency.

[0005] CN110213279A discloses a privacy protection method based on state decomposition, which divides the true state x of each node into two types: explicit and implicit states. Used for communication between nodes, implicit state For privacy protection, a bidirectional communication link exists between the explicit and implicit states. In the above method, both explicit and implicit states can asymptotically converge to the expected average value, and the true state is not revealed to neighboring nodes or external attackers. However, this requires that good nodes in the network must have a friendly neighbor, and adding internal nodes increases the communication burden, leading to network topology complexity and increased communication costs.

[0006] CN113300828B discloses a privacy protection method based on differential privacy. This method achieves strict privacy protection for the initial state of all nodes in a theoretical sense by introducing controlled noise into the information transmitted by nodes. That is, regardless of the attacker's computational power and observation methods, it is impossible to accurately infer the true initial value of any node. However, the differential privacy mechanism requires the introduction of additional random perturbations in each iteration and maintaining a strict balance between noise intensity and privacy budget, which significantly increases the algorithm's complexity in practice. Furthermore, frequent noise injection places higher demands on computational power and energy consumption, making this type of method difficult to implement efficiently in large-scale networks or resource-constrained scenarios. Although differential privacy can achieve global privacy protection in a strict sense, its cost in terms of complexity and computational power consumption cannot be ignored. Summary of the Invention

[0007] This invention provides an approximate average consensus method for privacy protection in networked systems, which offers strong privacy protection capabilities and low algorithm complexity. This invention also provides corresponding networked systems and software products.

[0008] The technical solution of this invention is as follows: A privacy-preserving approximate average consensus method for networked systems, wherein the communication structure of the networked system is an undirected connected graph, all nodes in the networked system iterate synchronously, and the iteration operation of a single node is as follows:

[0009] Randomly generate a first mask and a second mask, satisfying that the difference between the first mask and the common constant is absolutely summable, the second mask is absolutely summable, and the common constant is non-zero;

[0010] Calculate the product of the first mask and the current state, add the product to the second mask to obtain the outgoing transmission amount, and send the outgoing transmission amount to the neighboring nodes;

[0011] The received outgoing transmission volume and the outgoing transmission volume itself are weighted and summed according to a preset weight. The preset weight of the weighted sum is greater than 0 and the sum is 1. The weighted sum is divided by the common constant to obtain the update volume. The weight matrix of the networked system is a symmetric matrix.

[0012] The updated state value is obtained by weighted summation of the update amount and the initial state value. The weights of the weighted summation are fixed values, greater than 0, and the sum is 1.

[0013] In some implementations, the first mask and the second mask are randomly generated in the following manner:

[0014] Random sampling within a bounded interval yields a first initial mask; random sampling within a bounded interval yields a second initial mask.

[0015] The absolute values ​​of the first initial mask and the second initial mask are decayed according to a preset function while keeping the sign unchanged. The decayed first initial mask is added to the common constant to obtain the first mask. The decayed second initial mask is used as the second mask, wherein the decay rate increases with the number of iterations.

[0016] In some implementations, the first mask and the second mask are calculated according to the following formula:

[0017]

[0018] Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask for node i in the k-th iteration, ε is the common preset decay factor, and b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

[0019] In some implementations, the first mask and the second mask are calculated according to the following formula:

[0020]

[0021] Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask for node i in the k-th iteration, ε is the common preset decay factor, and b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

[0022] In some implementations, the first mask and the second mask are calculated according to the following formula:

[0023]

[0024] Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask of node i in the k-th iteration, b i (k) is the second mask of node i in the k-th iteration, βi (k) is the second initial mask of node i in the kth iteration.

[0025] In some implementations, the state of a node at least represents its location, motion parameters, energy consumption, or inventory.

[0026] In some implementations, the weights for the weighted summation of the initial state, the first mask, the second mask, the update amount, and the initial state value are all local private.

[0027] In some implementations, the initial state, the first initial mask, the first mask, the second initial mask, the second mask, the value range of the first initial mask and the second initial mask, and the weight of the weighted sum of the update amount and the initial state value are all local private.

[0028] The technical solution of the present invention is as follows: a networked system comprising multiple nodes, wherein the communication structure of the networked system is an undirected connected graph, all nodes in the networked system iterate synchronously, each node comprising a memory and a processor, wherein the memory stores a program, and the processor runs the program to execute the above-described method.

[0029] The technical solution of the present invention is as follows: a program product for running on nodes in a networked system, wherein the communication structure of the networked system is an undirected connected graph, and the program product executes the above-described method when running.

[0030] The privacy-preserving approximate average consensus method for networked systems of this invention has strong privacy protection capabilities and low method complexity. The limit value of the node's state value is approximately the average of the initial state values ​​of all nodes. Attached Figure Description

[0031] Figure 1 This is a flowchart of the approximate average consensus method for privacy protection in a networked system according to the present invention.

[0032] Figure 2 This is a network structure diagram of a networked system of a test example of the present invention.

[0033] Figure 3 This is a curve showing the change of the state values ​​of five nodes with the number of iterations in the test example of this invention. The horizontal axis k represents the number of iterations, and the vertical axis x... i [k] represents the state value of node i after the kth iteration.

[0034] Figure 4 Iterative graph of the difference in outgoing information before and after the initial state value of node i changes.

[0035] Figure 5 This is a structural block diagram of the nodes. Detailed Implementation

[0036] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0037] The following explanation uses a scalar state value as an example. When the state value is a vector, each component of the state value is updated iteratively and independently, and the update method is the same as that for a scalar state value.

[0038] The communication structure of a networked system is an undirected connected graph, and all nodes in the networked system iterate synchronously. A networked system with N nodes can be represented by an undirected connected topology graph G = (V, E), where V = {1, 2, ..., N} represents the nodes and edge set in the networked system. For any node {i,j∈V:(i,j)∈E}, nodes i and j can communicate with each other. Let N be the node name. i ={j∈V:(i,j)∈E} is the set of neighbors of node i, |N i | represents the number of elements in the neighbor set of node i.

[0039] Each node has a state value, which can represent its position, motion parameters, energy consumption, or inventory level. Specifically, a node's state value can represent one or more of the following: coordinates, orientation, velocity, acceleration, angular velocity, and angular acceleration. For example, a node's state value can represent a power plant's power generation, a factory's energy consumption, a warehouse's inventory level, or a road segment's traffic flow.

[0040] Each node corresponds to a computing device, which can be a computer, server, drone, unmanned boat, autonomous navigation transport vehicle, intelligent driving car, smart home, edge computer set up on one side of the road segment for intelligent driving, or other types of intelligent agents.

[0041] refer to Figure 1 The iteration operation for a single node is as follows:

[0042] S1. Randomly generate a first mask and a second mask, satisfying that the difference between the first mask and the common constant is absolutely summable, the second mask is absolutely summable, and the common constant is non-zero.

[0043] The first and second masks are local private and not publicly disclosed. Public constants are globally shared parameters; even if they were publicly disclosed, it would not affect the system's privacy protection capabilities. The difference between the first mask and the public constant is absolutely summable, meaning that as the number of iterations increases from 0 to positive infinity, the sum of the absolute values ​​of the differences between the first mask and the public constant is a finite value. The second mask is absolutely summable, meaning that as the number of iterations increases from 0 to positive infinity, the sum of the absolute values ​​of the second mask is a finite value.

[0044] The symbols are represented as follows: ∑ k |b i(k)|<∞, where k represents the iteration number, a i (k) represents the first mask of node i in the k-th iteration. b is a common constant. i (k) represents the second mask of node i in the kth iteration.

[0045] S2. Calculate the product of the first mask and the current state, add the product to the second mask to obtain the outgoing transmission amount, and send the outgoing transmission amount to the neighboring nodes.

[0046] The amount of data sent out by node i∈V in the kth iteration is y. i (k) is defined as: y i (k)=a i (k)x i (k)+b i (k), where x i (k) represents the current state of node i∈V, which is the state value before the kth iteration.

[0047] Since the first and second masks are random numbers, x i (k) has infinitely many possible values ​​for y, all of which yield the same result. i (k).

[0048] As the number of iterations increases, y i (k) approaches infinity Outbound transmission volume is equivalent to Random perturbations are added to the existing model, and the degree of perturbation tends to decrease as the number of iterations increases.

[0049] S3. The received outgoing transmission volume and the outgoing transmission volume sent by itself are weighted and summed according to a preset weight. The preset weight of the weighted sum is greater than 0 and the sum is 1. The weighted sum result is divided by the common constant to obtain the update volume. The weight matrix of the networked system is a symmetric matrix.

[0050] Define the weight matrix W = [w ij ]∈R N×N It satisfies: w ij ≥0; w ij =w ji ;when time w ij =0; w ij w is the preset weight between nodes i and j. ii Let be the weight of node i with respect to itself. This definition means that the preset weights of node i with non-neighboring nodes and with itself are 0. Therefore, for nodes that can send outgoing data to node i, their preset weights with node i are greater than 0.

[0051] The update amount of node i in the kth iteration is z i (k), This update amount can also be called the local aggregation amount.

[0052] The vectorized form of the update quantities of all nodes in the networked system at the k-th iteration is z(k): Let y(k) represent the sequence of all outgoing data from all nodes, then we have

[0053] S4. The updated value and the initial state value are weighted and summed to obtain the updated state value. The weights of the weighted sum are fixed values, greater than 0, and the sum is 1.

[0054] The symbol is represented as follows: x i [k+1]=λ i s i +(1-λ i )z i [k], s i Let λ be the initial state of node i. i Let λ be the stubbornness coefficient of node i, which serves as the weight in the weighted summation. λ represents the degree to which node i stubbornly maintains its initial state when updating its own state, where 0 < λ. i <1,x i [k+1] represents the state value of node i after the i-th iteration, which is also the state value before the k+1-th iteration.

[0055] Each time a node updates its own state, it does so at a fixed value λ. i s i Add offset (1-λ) to the base i )z i [k].

[0056] In vectorized representation, let the state x[k] of all nodes in the networked system before the i-th iteration be: Then the parallel iteration of all nodes can be uniformly written as a vector form update: x[k+1]=Λs+(I-Λ)z[k]; the stubbornness matrix Λ=diag(λ1,…,λ N Initial state vector I is the identity matrix.

[0057] The initial state, first mask, second mask, and stubbornness coefficient must all be local private.

[0058] The algorithm of this invention can deal with two types of attack models: one is honest but curious nodes, which follow the protocol to execute update rules, but will try to infer the private state of their neighbors from the information they receive; the other is eavesdroppers, who do not participate in the iterative process, but obtain sensitive information by listening to the data transmitted in the network.

[0059] Privacy protection capabilities are enhanced by the mask design, ensuring the non-uniqueness of initial value inference. Within any finite number of iterations k = 0, ..., T-1, different initial values ​​combined with different masks {a} i (k),b i (k)} can form the same outward transmission sequence, and both honest but curious neighbors and eavesdroppers can only observe the outward transmission amount y. i (k) and common constants And public weight W = [w ij The initial value x cannot be derived from this. i [0]. And because ∑ k |b i (k)| Finite, the first and second masks are equivalent to absolutely summable perturbations at the system level, and will not change the limiting solution of the consensus algorithm when the maskless design is used.

[0060] The following demonstrates the limiting state value of the method of the present invention.

[0061] The second step above is equivalent to applying a masking operation to the outward transmission. If no masking operation is applied to the outward broadcast (in this case, the networked system is a maskless system), then z = Wx. The operators A and H are defined as follows, along with the fixed point x. ★ A = (I - Λ)W, H = (IA) -1 Λ, x ★ :=Hs. Fixed point x ★ This represents the limit vector of the state of each node when z = Wx is used as the update variable. In a maskless system, the state vectors of all nodes are distinguished by the superscript nom, and the states of all nodes are iteratively updated according to the following formula: x nom [k+1]=Λs+(I-Λ)Wx nom [k], it is easy to prove that the spectral radius ρ((I-Λ)W)<1 (the spectral radii of I and W are 1, and the spectral radius of Λ is less than 1), thus obtaining x nom (k)→x ★ .

[0062] The outgoing transmission vector of the networked system provided in this embodiment of the invention is rewritten as follows: in The deviation of the outward transmission volume of the networked system of the present invention relative to the maskless system is expressed as x[k+1]=Λs+(I-Λ)Wx[k]+u(k), where x[k+1]=Λs+(I-Λ)Wx[k]+u(k) is defined as follows: Define e(k) = x[k] - x ★ , representing the error between the state of the networked system and the limit value of the state of the maskless system provided in the embodiments of the present invention. We can obtain e(k+1)=Ae(k)+u(k), A:=(I-Λ)W.

[0063] Define the supremum of the set of absolute values ​​of matrix eigenvalues ​​as the spectral radius ρ. Since ρ((I-Λ)W)<1, e(k)→0, the system converges and its limit is: x[∞]=[I-(I-Λ)W] -1 Λx[0]. The state limit value results are consistent with the state limit values ​​of the maskless system.

[0064] The mean of the initial state values ​​of all nodes is defined as follows: The error between the mean of the state limit vectors of each node and the initial state values ​​is: The upper bound of this error is: It is a finite, tiny, and definite value. H = (IA) was defined earlier. -1 Λ, A=(I-Λ)W, this supremum is controlled by the stubbornness matrix Λ. The smaller the stubbornness coefficient, the closer the limit value of the state value of each node is to the mean of the initial state value.

[0065] In summary, the method of this invention enables the state limit values ​​of each node to converge to near the mean of the initial state values. This invention is an approximate average consensus method.

[0066] In embodiments of the present invention, the first mask and the second mask are randomly generated in the following manner:

[0067] Random sampling within a bounded interval yields a first initial mask; random sampling within a bounded interval yields a second initial mask.

[0068] The absolute values ​​of the first initial mask and the second initial mask are decayed according to a preset function while keeping the sign unchanged. The decayed first initial mask is added to the common constant to obtain the first mask. The decayed second initial mask is used as the second mask, wherein the decay rate increases with the number of iterations.

[0069] This is equivalent to applying a gradually decaying random perturbation to each of the common constants and 0. It is necessary to satisfy the following conditions: the initial state, the first initial mask, the first mask, the second initial mask, the second mask, the value ranges of the first and second initial masks, and the stubbornness coefficients are all locally proprietary.

[0070] The following examples illustrate the methods for generating the first and second masks.

[0071] Mask generation method 1: The first mask and the second mask are calculated according to the following formula:

[0072]

[0073] Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask for node i in the k-th iteration, ε is the common preset decay factor, and b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

[0074] Mask generation method 2: The first mask and the second mask are calculated according to the following formula:

[0075]

[0076] Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask for node i in the k-th iteration, ε is the common preset decay factor, and b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

[0077] Mask generation method 3: The first mask and the second mask are calculated according to the following formula:

[0078]

[0079] Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask of node i in the k-th iteration, b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

[0080] The privacy protection capability of the method of this invention is demonstrated below. Specifically, mask generation methods 1 and 2 are used as examples for the demonstration; the demonstration approach is the same for other mask generation methods.

[0081] The single quote above the following symbols indicates the replacement value for the corresponding physical quantity.

[0082] The eavesdropper is aware of the following publicly available information: (G,W, ε, algorithm structure), where graph G = (V, E) represents the model of the networked system, and W = [w ij ] is the weight matrix. It is a common constant, and ε>0 is a preset decay factor. Within a finite time window k=0,1,…,T-1, an eavesdropper can detect the entire network's outgoing broadcast sequence {y}. r (t): r∈V, k=0,1,…,T-1}, honest but curious nodes can only observe the outgoing sequence {y} within their own visible range. r (t): r∈O, k=0,1,…,T-1 where It is an observable node that is honest but curious, and an honest but curious node can also observe its own state sequence {x}. r (t):r∈O c ,k=0,1,…,T-1}, where It is a set of honest but curious nodes. The set of information that honest but curious nodes and eavesdroppers can obtain is defined as follows:

[0083]

[0084] For target node i, let Ξ(i) be the set of possible initial values ​​under the premise that all visible information is completely consistent, assuming that honest but curious nodes and eavesdroppers coexist. T The discernible diameter of the possible initial value set is defined as DiffΞ(I,i). T ,i):=sup{|x i (0)-x' i (0)|:x i (0),x' i (0)∈Ξ(I T ,i)}, where sup is the function that takes the maximum value, representing |x i (0)-x' i The maximum value of (0)|, x i (0) and x' i (0) represents any two possible initial values ​​of node i.

[0085] The larger the discernible diameter of the system, the stronger its privacy protection capability. When DiffΞ(I) T When i) = ∞, the system is considered to have strong privacy.

[0086] Furthermore, the method provided by this invention has strong privacy protection. Given any reference value for the amount of data sent outward and a finite window k = 0, 1, ..., T-1, for any target node v i and replacing the initial value x' i (0), simply adjust the mask to its value. achievable This represents the outbound transmission volume corresponding to the original initial value before the initial value was replaced, y' i (k) represents the outgoing transmission volume after replacing the initial value, a' i (k) and b' i (k) represents the first and second masks generated after replacing the initial value. Therefore, when an honest but curious node and an eavesdropper coexist, the visible information is completely identical, and the initial state value of the target node cannot be uniquely deduced within any finite window.

[0087] Refer to the previous definition of a fixed point x ★ Define parameter z ★ =Wx ★ , representing the limit of the update quantity of the maskless system, for any node i and any stubbornness coefficient λ' i ∈(0,1), Limit equation Equivalent to Therefore, the set of reachable initial values ​​is from Depart, along the way One-sided rays, This indicates that each node uses z. ★ The state limit value of node i when used as the update quantity.

[0088] For any window T, the target node i has DiffΞ(I) when both the eavesdropper and the honest and curious node are present. T If (i) = ∞, the system has strong privacy and the convergence point remains unchanged.

[0089] <Test Example>

[0090] As an example of this invention, a ring network consisting of 5 agents is defined, and its topology is as follows: Figure 2 As shown, the topology is an undirected connected graph. The adjacency matrix B is then:

[0091] The stubbornness coefficients of the five nodes are set to 0.003, 0.004, 0.005, 0.006, and 0.007 respectively. The initial state vector x = [-10.51.20.8-0.3] is formed by the initial values ​​of all nodes.

[0092] Each node generates its outgoing transmission volume according to mask generation method 1, and the state convergence curve can be obtained, such as... Figure 3 As shown, the method of this invention has excellent convergence results, and the results of repeated experiments are the same, indicating precise convergence.

[0093] To demonstrate the effectiveness of the privacy protection method proposed in this invention, node v has been modified without loss of generality. i initial value and stubbornness λ i Furthermore, a mask was redesigned to conform to the method proposed in this invention and iterated upon. Figure 4 Given ||y'(k)-y ref (k)|| ∞ (This represents the replacement value y'(k) of the outgoing data volume and the reference value y) ref The infinite norm of (k) yields numerical results for k = 0, ..., T-1, with the curve always being 0, down to machine precision. This means that for any honest but curious neighbor or arbitrary eavesdropper, regardless of their discernible radius, the visible data is exactly the same within this finite observation window. Therefore, the information set cannot distinguish {x} i (0),a i (k),b i (k)} and the corresponding replacement value {x' i (0),a' i (k),b' i (k)} These two sets of parameters, the initial target value x i [0] and the corresponding replacement value x' i [0] = x i [0]+c forms a non-single-point equivalence class, which is therefore not uniquely identifiable within the window, where c is the offset.

[0094] Based on the same inventive concept, embodiments of the present invention also provide a networked system, including multiple nodes. The communication structure of the networked system is an undirected connected graph, and all nodes in the networked system iterate synchronously. (Refer to...) Figure 5 The node includes a memory and a processor, the memory storing a program and the processor running the program to perform the method described above.

[0095] Based on the same inventive concept, embodiments of the present invention also provide a program product for running on nodes in a networked system, wherein the communication structure of the networked system is an undirected connected graph, and the program product executes the aforementioned method when running.

[0096] The processor may include, but is not limited to, one or more processors or microprocessors. Each processor may be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor (MCU), central processing unit (CPU), graphics processing unit (GPU), or other electronic components to perform the methods described in the above embodiments.

[0097] The above-mentioned storage devices can be various media that can store program code, such as USB flash drives, fixed hard drives, portable hard drives, read-only memory (ROM), random access memory (RAM), flash memory, EPROM memory, EEPROM memory, registers, magnetic disks or optical disks.

[0098] This invention is not limited to the above-described embodiments. Any modifications, improvements, or substitutions that can be conceived by those skilled in the art without departing from the essential content of this invention fall within the scope of this invention.

Claims

1. A privacy-preserving approximate average consensus method for networked systems, characterized in that, The communication structure of a networked system is an undirected connected graph. All nodes in the networked system iterate synchronously. The iteration operation of a single node is as follows: Randomly generate a first mask and a second mask, satisfying that the difference between the first mask and the common constant is absolutely summable, the second mask is absolutely summable, and the common constant is non-zero; Calculate the product of the first mask and the current state, add the product to the second mask to obtain the outgoing transmission amount, and send the outgoing transmission amount to the neighboring nodes; The received outgoing transmission volume and the outgoing transmission volume itself are weighted and summed according to a preset weight. The preset weight of the weighted sum is greater than 0 and the sum is 1. The weighted sum is divided by the common constant to obtain the update volume. The weight matrix of the networked system is a symmetric matrix. The updated state value is obtained by weighted summation of the update amount and the initial state value. The weights of the summation are fixed values, greater than 0, and the sum is 1.

2. The method according to claim 1, characterized in that, The first and second masks are randomly generated as follows: Random sampling within a bounded interval yields a first initial mask; random sampling within a bounded interval yields a second initial mask. The absolute values ​​of the first initial mask and the second initial mask are decayed according to a preset function while keeping the sign unchanged. The decayed first initial mask is added to the common constant to obtain the first mask. The decayed second initial mask is used as the second mask, wherein the decay rate increases with the number of iterations.

3. The method according to claim 2, characterized in that, The first mask and the second mask are calculated according to the following formula: Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask for node i in the k-th iteration, ε is the common preset decay factor, and b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

4. The method according to claim 2, characterized in that, The first mask and the second mask are calculated according to the following formula: Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask for node i in the k-th iteration, ε is the common preset decay factor, and b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

5. The method according to claim 2, characterized in that, The first mask and the second mask are calculated according to the following formula: Where k is the iteration number, a i (k) is the first mask of node i in the k-th iteration. α is a common constant. i (k) is the first initial mask of node i in the k-th iteration, b i (k) is the second mask of node i in the k-th iteration, β i (k) is the second initial mask of node i in the kth iteration.

6. The method according to claim 1, characterized in that, The state of a node at least represents its location, motion parameters, energy consumption, or inventory.

7. The method according to claim 1, characterized in that, The weights for the weighted summation of the initial state, first mask, second mask, update amount, and initial state value are all local private.

8. The method according to claim 2, characterized in that, The initial state, the first initial mask, the first mask, the second initial mask, the second mask, the value range of the first initial mask and the second initial mask, and the weights for the weighted summation of the update amount and the initial state value are all local private.

9. A networked system comprising multiple nodes, wherein the communication structure of the networked system is an undirected connected graph, and all nodes in the networked system iterate synchronously, characterized in that... The node includes a memory and a processor, the memory storing a program and the processor running the program to perform the method according to any one of claims 1 to 8.

10. A program product, characterized in that, It is used for nodes running in a networked system, the communication structure of which is an undirected connected graph, and the program product executes the method according to any one of claims 1 to 8 when it runs.

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