Privacy protection method for linear quadratic control system based on model perturbation

Abstract

The application provides a privacy protection method of a linear quadratic control system based on model disturbance, and comprises the following steps: intentionally informing a cloud of an incorrect system model according to the problem setting that system knowledge between the cloud and a client is asymmetric; introducing a system observation matrix error, and widening the coverage of the privacy protection method design under the condition that the system knowledge between the cloud and the client is asymmetric according to the existing state estimation inherent error boundary and the existing privacy protection method; the client sends processed data to the cloud instead of the original information sequence of the local system; and according to a linear quadratic Gaussian problem, the influence of the collaborative design of the linear transformation and the model parameter disturbance on the privacy protection and control performance trade-off is obtained.

Description

Technical Field

[0001] This invention relates to the field of network security technology, and in particular to a privacy protection method for a linear quadratic control system based on model perturbation. Background Technology

[0002] Networked control systems are spatially distributed systems where communication between sensors, actuators, and controllers occurs through a shared digital communication network. Given the convenience of shared digital communication networks, networked control systems are increasingly widely used in smart grids, manufacturing systems, process control, and intelligent transportation. Cloud services can enable collaborative configuration of networked control systems; however, due to the complexity of the system architecture and its dependence on communication networks, the data availability, integrity, and confidentiality of networked control systems are inevitably threatened and compromised. Therefore, it is necessary to design effective privacy-protecting security control schemes under network constraints to improve the reliability and security of networked control systems. Summary of the Invention

[0003] The purpose of this invention is to provide a privacy protection method for linear quadratic control systems based on model perturbation, so as to design an effective privacy protection security control scheme under network constraints and improve the reliability and security of network control systems.

[0004] To address the aforementioned technical problems, this invention provides a privacy protection method for linear quadratic control systems based on model perturbations, comprising:

[0005] By introducing the system observation matrix error, and estimating the inherent error bound based on the existing state and existing privacy protection methods, the coverage of privacy protection method design under the condition of knowledge asymmetry between cloud and client systems is broadened.

[0006] The client sends processed data to the cloud, replacing the original information sequence from the local system.

[0007] Based on the linear quadratic Gaussian problem, we obtain the impact of the co-design of linear transformation and model parameter perturbation on the tradeoff between privacy protection and control performance.

[0008] Optionally, the privacy protection method for the linear quadratic control system based on model perturbation further includes:

[0009] Step 1: Define a discrete linear time-invariant control system; the client provides a static information set and real-time dynamic data so that the control end can process the information and output control signals; first, establish the following dynamic model of the client system:

[0010]

[0011] Among them is The system's state transition matrix, It is a control matrix. It is the observation matrix. It is the initial state. It's process noise. It is observation noise; the system state and noise distribution are independent of each other, and the system is stable and measurable.

[0012] Optionally, the privacy protection method for the linear quadratic control system based on model perturbation further includes:

[0013] Step 2: Based on the system model in Step 1, we obtain the "honest but curious" cloud, which means that the cloud performs control operations in a pre-given manner, but will infer the client's private information. The client transmits the raw observation data to the cloud to ensure ideal control performance, while facing the risk of information leakage.

[0014] When faced with an untrusted cloud, the client provides the cloud with incorrect model knowledge, meaning that the cloud's information set and the client's information set differ only in the observation matrix.

[0015] Client information set is The information set in the cloud is In addition, to protect data privacy, the local client transmits the observations, which have undergone linear transformation, to the cloud.

[0016] It is the client-side minimum mean square error prior state estimate, and the state iteration follows the traditional Kalman filter.

[0017]

[0018] in It is the system's information sequence. These are the prior and posterior state estimates of the system from the local client. , It is the prior and posterior estimation error covariance of the client. It is the Kalman filter gain on the client side;

[0019] In this problem, the cloud is completely unaware of the system model error, so the cloud uses the same Kalman filter method to estimate based on the erroneous observation matrix state;

[0020] in It is the sequence of new information received by the cloud. It is the cloud's estimation of the system's posterior state. It is the posterior estimation error covariance of the cloud. It is the Kalman filter gain of the cloud;

[0021] Define the true posterior estimation error covariance in the cloud:

[0022]

[0023] where is the true state of the system.

[0024] Optionally, in the privacy protection method of the model disturbance-based linear quadratic control system, further comprising:

[0025] Step three: the cost function of the finite time linear quadratic control system is defined as follows:

[0026]

[0027] where , is the weight matrix of the linear quadratic control, defined by the client;

[0028] The linear dynamic system and the quadratic cost function together constitute a linear quadratic Gaussian control problem, and the optimal controller is:

[0029]

[0030] where , Follow the following update criteria:

[0031] , ;

[0032] Because the cloud is "honest", the cloud will transmit the control input calculated according to the above iterative process to the client for state update, that is ; Since there is an error in the state estimation, this control input is obviously suboptimal, and the control performance loss is defined as:

[0033]

[0034] where is the quadratic cost function under the optimal control, and similarly is the steady-state performance loss;

[0035] Consider the deviation of the state estimation of the system by the cloud and the client as privacy, then the privacy metric is

[0036] ,

[0037] where , then is the steady-state estimation deviation, which is also the steady-state privacy index.

[0038] Optionally, in the privacy protection method of the model disturbance-based linear quadratic control system, further comprising:

[0039] Step four: Study the impact of the collaborative design of linear transformation and model parameter perturbation on the privacy protection and control performance trade-off; First, this trade-off problem is formulated as an optimization problem that maximizes privacy protection as much as possible under the requirement of a certain control performance loss;

[0040] P1

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] wherein , , is a predefined constant indicating that the observation matrix of the cloud cannot deviate too far from the true value, and linear perturbation is considered here; the client uses a sparse matrix to linearly transform the innovation sequence to reduce the computational burden; in a strict sense, the number of non-zero elements in the matrix is represented by the 0-norm, but since the solution of the 0-norm is NP-Hard, the sparsity of the matrix is represented by the -norm.

[0047] Optionally, in the privacy protection method for the linear quadratic control system based on model perturbation, further comprising:

[0048] Step five: For the solution of the optimization problem in step four, first derive the accurate expressions of the privacy index and the control performance loss;

[0049] The privacy index satisfies the following Lyapunov equation:

[0050]

[0051] The control quadratic cost function and the privacy index satisfy the following equation:

[0052]

[0053] wherein ;

[0054] In the infinite time domain linear quadratic control system, the control performance loss and the privacy index satisfy

[0055]

[0056] wherein ;

[0057] In the scalar system, after the explicit expression of the privacy index and the control performance loss, the optimization problem in step four is directly solved; the solution of the optimization problem is the linear transformation matrix and the observation matrix disturbance ;

[0058]

[0059]

[0060] The optimal target is ;

[0061] Where , are the steady-state prior state estimation covariance of the local client and the cloud, respectively.

[0062] Optionally, in the privacy protection method of the linear quadratic control system based on model disturbance, further comprising:

[0063] Step six: In the multi-dimensional system, it is difficult to directly solve the optimization problem in step four, because in the multi-dimensional system, the Lyapunov equation satisfied by the privacy index has no analytical solution;

[0064] From step five, given the upper bound of the system control performance loss, there are multiple pairs of linear transformation matrix and observation matrix disturbance solutions, and further explore the relationship between the two; in all feasible solutions, in order to save computing resources, the sparsity of the linear transformation matrix is taken as the optimization problem objective function;

[0065] By scaling the optimization problem, the trade-off between control performance loss and privacy index is transformed into the sparsity of the linear transformation matrix, and the problem is transformed into the design of system model disturbance and linear transformation under the premise of given control performance loss;

[0066] P2

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Further integrate and transform the restriction conditions in the optimization problem, and the linear transformation matrix satisfies the following restriction conditions

[0073]

[0074] wherein, , , , , represent the maximum singular value of ; represent the maximum eigenvalue of , represent the minimum eigenvalue of , represent the maximum eigenvalue of ;

[0075] Convert the optimization problem in step four into a sparse problem of linear transformation matrix:

[0076] P3

[0077]

[0078]

[0079]

[0080]

[0081] Because of its good convexity, use the solving tool to solve directly.

[0082] Optionally, in the privacy protection method based on model disturbance of the linear quadratic control system, further comprising:

[0083] Introducing model parameter disturbance into the privacy protection method, and performing privacy protection according to the model knowledge asymmetry between the local client and the cloud;

[0084] In order to realize the privacy protection of defending the cloud speculation, the system model information disturbance is introduced, the existing privacy protection method is understood from the angle of system information asymmetry, the false noise covariance is introduced, the system model disturbance is introduced, and the privacy protection method is widened Collaborative design;

[0085] Under the condition of bottom layer model information asymmetry, the trade-off problem between control system performance loss and privacy index is converted into a sparse problem of linear transformation matrix, and in step four, a privacy protection algorithm for cloud-based linear quadratic control system under model disturbance is designed as follows:

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] The communication interaction between the local and the cloud is a new information sequence derived from the observation information, and the connection of the system structure is considered to select the disturbance of the observation matrix in the system model parameter.

[0092] Optionally, in the privacy protection method of the linear quadratic control system based on model disturbance, further comprising:

[0093] In the case of asymmetric model knowledge, a linear transformation method is designed to jointly design sparse transformation, bottom model disturbance and upper sparse transformation of the new information sequence transmitted by the client.

[0094] In step six,

[0095]

[0096]

[0097]

[0098]

[0099] The linear transformation method is applied to the upper strategy of the control system privacy protection to realize the conversion of the privacy and performance trade-off problem in the control system into the optimization problem of matrix sparsity, and reduce the system calculation amount.

[0100] Optionally, in the privacy protection method of the linear quadratic control system based on model disturbance, further comprising:

[0101] The privacy index is defined, and the deviation of the cloud state estimation and the real state estimation is taken as the privacy measurement, which is more suitable for the control performance of the networked control system.

[0102] The error-based measurement quantifies the error made by the cloud in estimating the system state. Because the calculation of these measurements requires information about the true results, only the local client can obtain them, in steps three and five,

[0103]

[0104]

[0105] Because the estimation error of the cloud can be directly linked to the control performance loss of the system, the error-based measurement is more suitable for the networked control system.

[0106] The inventor of the present application found that the existing research on privacy protection in the cooperative network control system has the following methods: random confusion method and deterministic transformation method. The random confusion method, such as differential privacy and adding artificial noise, the deterministic transformation method, such as homomorphic encryption, encoding and decoding technology. These methods achieve privacy protection by encrypting or adding noise to the original information sequence transmitted to the cloud, which inevitably loses computational complexity and control performance, so there is a trade-off between privacy protection and utility performance.

[0107] The existing privacy protection method is based on the symmetry of the system model knowledge between the cloud and the client, that is, the cloud completely masters the system knowledge. In actual application occasions, the cloud's understanding of the system model is not accurate enough. In the case of asymmetric model knowledge between the two parties, the influence of such errors on the privacy protection performance of the system has not been considered.

[0108] To evaluate the influence of privacy protection behavior on the performance of the control system, the core problem is to quantify the degree of privacy protection. Concepts such as entropy and mutual information in information theory are often used to characterize the degree of privacy protection, but such work often focuses on inferring the conditional probability of private information based on prior knowledge. These indicators generally depend on strong assumptions. Another type of evaluation index is differential privacy, which is suitable for centralized models with multiple participants. It is easier to demonstrate the degree of privacy protection in static data in the database. However, in the case of non-static data in a non-stable environment, or when the perturbation term is not input data, it is difficult to demonstrate that the method meets the privacy definition.

[0109] Based on the above insights, the present application provides a privacy protection method for linear quadratic control systems based on model perturbation. According to the problem setting that the system knowledge between the cloud and the client is asymmetric, that is, the client intentionally informs the (honest but curious) cloud of the wrong system model in order to protect privacy. The privacy protection method design considers the concept of model uncertainty in robust control and applies it to the study of privacy protection. The error of the system observation matrix is introduced, and the existing privacy protection method is combined with the inherent error bound of state estimation to broaden the coverage of the privacy protection method design in the case of asymmetric system knowledge between the cloud and the client in practical application occasions. In addition, the client will send processed data to the cloud instead of the original information sequence of the local system. Specifically, a linear transformation is performed on the transmitted data. Taking the linear quadratic Gaussian (LQG) problem as the background, the influence of the cooperative design of linear transformation and model parameter perturbation on the trade-off between privacy protection and control performance is studied. Therefore, it has the following advantages:

[0110] First, the deviation of the cloud's system state estimation and the system's actual state estimation is taken as the privacy protection metric, instead of a probability distribution, which is more suitable for the common concept in the research of networked control systems. Compared with differential privacy, this metric can also be directly applied to the case of a single user.

[0111] Second, the observation matrix perturbation and linear transformation strategy are designed cooperatively to achieve the trade-off between privacy protection and control performance. The client performs linear transformation on the observation data. In the scalar case, the optimal cooperative design of linear transformation and model parameter perturbation is studied, and the optimal solution of the trade-off problem can be obtained. In the multi-dimensional scenario, the sparsity of the linear transformation matrix is considered to reduce the client's computation, and the cooperative design problem is redefined as a convex optimization problem. BRIEF DESCRIPTION OF DRAWINGS

[0112] Figure 1 is the flow chart of the privacy protection method of the linear quadratic control system based on model perturbation in an embodiment of the present application;

[0113] Figure 2 is the privacy protection schematic diagram of the local client using model parameter perturbation and linear transformation in an embodiment of the present application. DETAILED DESCRIPTION

[0114] The present application will be further described below in conjunction with the specific embodiments and the accompanying drawings.

[0115] It should be noted that the components in the drawings can be exaggerated for illustration, and are not necessarily to scale. In the drawings, the same or similar components are provided with the same reference numerals.

[0116] In the present application, unless specifically indicated, "arranged on", "arranged above" and "arranged over" do not exclude the presence of an intermediate object between them. In addition, "arranged on or above" only indicates the relative position relationship between the two components, which can be converted to "arranged below or below" in some cases, such as after reversing the product direction, and vice versa.

[0117] In the present application, each embodiment is only intended to illustrate the scheme of the present application, and should not be understood as limiting.

[0118] In the present application, unless specifically indicated, the quantifier "one" does not exclude the scenario of multiple elements.

[0119] It should also be noted that, in the embodiments of the present application, only a part of components or assemblies can be shown for the purpose of clarity and simplicity, but those skilled in the art can understand that, under the teaching of the present application, the required components or assemblies can be added according to the specific scene. In addition, the features in different embodiments of the present application can be combined with each other unless otherwise stated. For example, a feature in the second embodiment can replace a corresponding or functionally similar feature in the first embodiment, and the resulting embodiment also falls within the disclosure or recitation range of the present application.

[0120] It should also be noted that, in the scope of the present application, the words "same", "equal", "equal to" and the like do not mean that the numerical values of the two are absolutely equal, but allow a certain reasonable error, that is, the words also cover "substantially the same", "substantially equal", "substantially equal to". By analogy, in the present application, the terms "perpendicular to", "parallel to" and the like also cover the meanings of "substantially perpendicular to", "substantially parallel to".

[0121] In addition, the numbering of the steps of the methods of the present application does not limit the execution order of the method steps. Unless specifically indicated, the method steps can be executed in different orders.

[0122] The privacy protection method of a linear quadratic control system based on model disturbance proposed by the present application will be further described in detail below in combination with the drawings and specific embodiments. According to the following description, the advantages and features of the present application will be more apparent. It should be noted that the drawings are very simplified and use non-precise proportions, only for the purpose of facilitating and clearly assisting the description of the embodiments of the present application.

[0123] The present application aims to provide a privacy protection method of a linear quadratic control system based on model disturbance, to realize the design of an effective privacy protection security control scheme under network constraints, and to improve the reliability and security of network control systems.

[0124] To achieve the above-mentioned purpose, the present application provides a privacy protection method of a linear quadratic control system based on model disturbance, comprising: intentionally informing the cloud of an incorrect system model according to the problem setting that the system knowledge between the cloud and the client is asymmetric; introducing a system observation matrix error, according to the existing state estimation inherent error bound and the existing privacy protection method, to broaden the coverage of the privacy protection method design under the condition that the system knowledge of the cloud and the client is asymmetric; the client sends processed data to the cloud instead of the original information sequence of the local system; according to the linear quadratic Gaussian problem, the influence of the collaborative design of linear transformation and model parameter disturbance on the privacy protection and control performance trade-off is obtained.

[0125] Figures 1-2 Embodiments of the present application are provided, Figure 1A flowchart of a privacy protection method for a linear quadratic control system based on model perturbation is shown.

[0126] like Figure 1 As shown, step one: Define a discrete linear time-invariant control system. The client provides a static information set (such as the system model, noise distribution, etc.) and real-time dynamic data, such as the system's information sequence, so that the control end can process the information and output control signals. First, establish the following client system dynamic model:

[0127]

[0128] Among them is The system's state transition matrix, It is a control matrix. It is the observation matrix. It is the initial state. It's process noise. This is observation noise. The system state and noise distribution are independent of each other, and the system is stable and measurable.

[0129] Step Two: Based on the system model in Step One, consider an "honest but curious" cloud. That is, the cloud dutifully performs control operations in a pre-given manner, but infers the client's private information. The client transmits raw observation data to the cloud to ensure ideal control performance, while facing the risk of information leakage.

[0130] When faced with an untrusted cloud, the client transmits incorrect model knowledge to the cloud; that is, the cloud's information set differs from the client's information set only in the observation matrix. The client's information set is... The information set in the cloud is In addition, to protect data privacy, the local client transmits the observations, which have undergone linear transformation, to the cloud.

[0131] It is the client-side minimum mean square error prior state estimate, and the state iteration follows the traditional Kalman filter.

[0132]

[0133] in It is the system's information sequence. These are the prior and posterior state estimates of the system from the local client. , It is the prior and posterior estimation error covariance of the client. It is the Kalman filter gain on the client side.

[0134] In this problem, the cloud is completely unaware of the system model errors; therefore, the cloud uses the same Kalman filtering method to estimate based on the erroneous observation matrix state.

[0135] where is the innovation sequence received by the cloud, is the cloud's posterior state estimate of the system, is the cloud's posterior estimation error covariance, is the cloud's Kalman filter gain.

[0136] Define the cloud's true posterior estimation error covariance as

[0137]

[0138] where is the system's true state.

[0139] Step three: The cost function of the finite-horizon linear quadratic control system is defined as

[0140]

[0141] where , is the weight matrix of the linear quadratic control, defined by the client.

[0142] The linear dynamics system and the quadratic cost function together form a linear quadratic Gaussian control problem, and the optimal controller is

[0143]

[0144] where , follows the update rule:

[0145] , .

[0146] Because the cloud is "honest", the cloud will transmit the control input calculated by the above iterative process to the client for state update, i.e. . Since there is an error in the state estimate, this control input is obviously suboptimal, and the control performance loss is defined as

[0147]

[0148] where is the quadratic cost function under the optimal control, and similarly, is the steady-state performance loss.

[0149] Consider the deviation of the cloud and the client's state estimates of the system as privacy, then the privacy measure is

[0150] ,

[0151] wherein then is the steady-state estimation bias, which is also the steady-state privacy indicator.

[0152] Step four: Study the impact of the collaborative design of linear transformation and model parameter perturbation on the privacy protection and control performance trade-off. First, this trade-off problem can be formulated as an optimization problem that maximizes privacy protection as much as possible under the given control performance loss requirement.

[0153] P1

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] wherein , , is a pre-defined constant indicating that the observation matrix of the cloud cannot deviate too far from the true value, and linear perturbation is considered here. The client uses a sparse matrix to linearly transform the innovation sequence to reduce the computational burden. In a strict sense, the 0-norm is used to represent the number of non-zero elements in the matrix (i.e., its sparsity). However, since the solution of the 0-norm is NP-Hard, the present invention uses the -norm to represent the sparsity of the matrix.

[0160] Step five: For the solution of the optimization problem in step four, first derive the accurate expressions of the privacy indicator and the control performance loss.

[0161] The privacy indicator satisfies the following Lyapunov equation:

[0162]

[0163] The control quadratic cost function and the privacy indicator satisfy the following equation:

[0164]

[0165] wherein .

[0166] In an infinite-time domain linear quadratic control system, the control performance loss and the privacy indicator satisfy

[0167]

[0168] wherein .

[0169] In the scalar system, after the explicit expression of the privacy index and the control performance loss, the optimization problem in step four can be solved directly. The solution of this optimization problem is the linear transformation matrix and the observation matrix perturbation pair .

[0170]

[0171]

[0172] The optimal objective is .

[0173] where , are the steady-state prior state estimation covariances of the local client and the cloud, respectively.

[0174] Step six: In the multi-dimensional system, it is difficult to directly solve the optimization problem in step four, because in the multi-dimensional system, the Lyapunov equation satisfied by the privacy index has no analytical solution, in addition, as can be seen from step five, given the upper bound of the system control performance loss, there are multiple pairs of linear transformation matrix and observation matrix perturbation solutions, and further exploration is needed to find the relationship between the two. In all feasible solutions, in order to save computing resources, the sparsity of the linear transformation matrix is taken as the objective function of the optimization problem.

[0175] By scaling the optimization problem, the trade-off between the control performance loss and the privacy index is transformed into the sparsity of the linear transformation matrix, and the problem is transformed into the collaborative design of the system model perturbation and the linear transformation under the premise of the given control performance loss.

[0176] P2

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] Further integrate and transform the constraints in the optimization problem, the linear transformation matrix satisfies the following constraints

[0183]

[0184] where, , , , . represent the maximum singular value of , represent the maximum eigenvalue of , represent the minimum eigenvalue of , represent the maximum eigenvalue of .

[0185] In summary, the optimization problem in step four can be transformed into a sparse problem of linear transformation matrix:

[0186] P3

[0187]

[0188]

[0189]

[0190]

[0191] Due to its good convexity, it can be directly solved using solving tools.

[0192] Improvement point 1: introduce model parameter disturbance into the privacy protection method, and consider the asymmetry of model knowledge between the local client and the cloud when studying privacy protection problems.

[0193] In order to realize the privacy protection against cloud speculation, the system model information disturbance is introduced in the application, and the existing privacy protection method such as adding noise is understood from the perspective of system information asymmetry, that is, introducing error noise covariance, introducing system model disturbance, and widening the privacy protection method collaborative design. Under the condition of bottom model information asymmetry, the trade-off problem between system performance loss and privacy index is transformed into a sparse problem of linear transformation matrix, and in step four, the following cloud-based linear quadratic control system privacy protection algorithm based on model disturbance is designed:

[0194]

[0195]

[0196]

[0197]

[0198]

[0199] The communication interaction between the local and the cloud is a new information sequence derived from the observation information, and the connectivity of the system structure is considered to select the disturbance of the observation matrix in the system model parameter.

[0200] Improvement point 2: In the case of asymmetric model knowledge, a linear transformation method is designed to sparsely transform the new information sequence transmitted by the client, and the joint design of the bottom model disturbance and the upper sparse transformation.

[0201] Due to the complexity of the networked control system and the dependence on the communication network, in order to realize the protection of the private state information of the system, several control methods are proposed in the prior art, such as the random confusion method and the deterministic transformation method. Compared with other encryption methods and the method of adding artificial noise, the sparse linear transformation is simple, intuitive in design, and has good robustness to uncertain parameters and disturbances of the system.

[0202] In step six,

[0203]

[0204]

[0205]

[0206]

[0207] The application applies the linear transformation method to the upper strategy of the privacy protection of the control system, realizes the conversion of the privacy and performance trade-off problem in the control system into the optimization problem of solving the sparsity of the matrix, and reduces the system calculation amount.

[0208] Improvement point 3: The definition of the privacy index, the deviation of the cloud state estimation and the real state estimation is taken as the privacy measurement, which is more suitable for the control performance of the networked control system.

[0209] The error-based measurement quantifies the error made by the cloud in estimating the system state. Because the calculation of these measurements requires information about the true result, only the local client can obtain it in steps three and five,

[0210]

[0211]

[0212] Since the estimation error of the cloud can be directly linked to the control performance loss of the system, the error-based measurement is more suitable for the networked control system.

[0213] Figure 2 It is a privacy protection scheme of the local client using model parameter disturbance and linear transformation, such as Figure 2As shown, the application is suitable for a cloud-based control system, in the face of an honest but curious cloud, the client realizes privacy protection by observing matrix disturbance and linear transformation of the transmission information. By the model information asymmetry between the cloud and the client, combined with existing privacy protection methods, a joint disturbance is formed.

[0214] Among them, in the scalar system, the optimal collaborative design of linear transformation and model parameter disturbance is given.

[0215] In the multi-dimensional system, while solving the trade-off between privacy protection and control performance, a sufficiently sparse linear transformation matrix is obtained, saving computing resources.

[0216] In summary, the above embodiments detail the different configurations of the privacy protection method of the linear quadratic control system based on model disturbance. Of course, the application includes but is not limited to the configurations listed in the above embodiments. Any transformation based on the configurations provided in the above embodiments belongs to the scope of the application. Those skilled in the art can draw conclusions from the above embodiments.

[0217] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part.

[0218] The above description is only a description of the preferred embodiments of the application, and does not limit the scope of the application. Any modification or modification made by those skilled in the art based on the above disclosure is within the scope of protection of the claims.

Claims

1. A privacy protection method for a model-based perturbed linear quadratic control system, characterized in that, Comprise: According to the asymmetric problem of system knowledge between the cloud and the client: the client deliberately informs the cloud of the wrong system model, which is the disturbed observation matrix obtained by linearly disturbing the real observation matrix C of the client inform the cloud, wherein, , is the observation matrix disturbance coefficient; A system observation matrix error is introduced, which is the deviation of a true observation matrix C and a perturbed observation matrix Based on the existing state estimation inherent error bound and the existing privacy protection method, the coverage of the privacy protection method design under the condition of asymmetric knowledge between the cloud and the client system is widened. The client sends the processed data to the cloud instead of the original information sequence of the local system: the client's innovation sequence of the local system Sparse linear transformation processing is performed to obtain the processed data and send it to the cloud to block the cloud from the source through the innovation sequence The path of the client's private information is deduced, and the processed data is wherein is a linear transformation matrix; and According to a linear quadratic Gaussian problem, obtain a linear transformation matrix and a perturbation observation matrix The effect of the collaborative design of the linear transformation matrix and the perturbation coefficient on the privacy protection and control performance trade-off is optimized.

2. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 1, wherein, Also comprise: Step one: define the discrete linear time-invariant control system; The client provides a static information set and real-time dynamic data for the control end to process information and output control signals; First, establish the following client system dynamic model: wherein the state transition matrix of the system, is the control matrix, is the observation matrix, is the initial state, is the process noise, is the observation noise; the state and noise distribution of the system are independent of each other, and the system is stable and measurable.

3. The method for privacy protection of a model-based perturbed linear quadratic control system of claim 2, wherein, Also comprise: Step two: according to the system model in step one, get the "honest but curious" cloud, that is, the cloud performs control operations in accordance with the pre-defined manner, but will infer the private information of the client, the client transmits the original observation data to the cloud to ensure the ideal control performance, while facing the risk of information leakage; In the face of untrusted cloud, the client will inform the cloud of the wrong model knowledge, that is, the information set of the cloud is only different from the observation matrix of the information set of the client; The client information set is , and the cloud information set is ; in addition, to protect data privacy, the local client transmits the observation values processed by linear transformation to the cloud; is the client's minimum mean square error prior state estimate, the state iteration follows the traditional Kalman filter wherein is the innovation sequence of the system, are the prior and posterior state estimates of the local client to the system, respectively, , are the prior, posterior estimation error covariances of the client, is the Kalman filter gain of the client; Under this problem, the cloud has no knowledge of the system model error, so the cloud estimates based on the wrong observation matrix state using the same Kalman filtering method; wherein is the innovation sequence received by the cloud, is the cloud's a posteriori state estimate of the system, is the cloud's a posteriori estimation error covariance, is the cloud's Kalman filter gain; Define the real posterior estimation error covariance of the cloud: wherein is the true state of the system.

4. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 3, wherein, Also comprise: Step three: the cost function of the finite time domain linear quadratic control system is defined as follows: wherein , is a weight matrix for linear quadratic control, defined by the client; The linear dynamic system and the quadratic cost function together constitute a linear quadratic Gaussian control problem, and the optimal controller is: wherein , The following update criteria are followed: ， ； Since the cloud is "honest", the cloud transmits the control input computed according to the above iterative procedure to the client for state update, i.e. ; since there is error in the state estimation, this control input is obviously suboptimal, define the control performance loss as: where is the quadratic cost function under optimal control, and is the steady-state performance loss; Consider the deviation of the cloud and the client's state estimation of the system as privacy, and the privacy metric is ， where then is the steady-state estimation bias, which is also the steady-state privacy indicator.

5. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 4, wherein, Also comprise: Step four: study the influence of the collaborative design of linear transformation and model parameter disturbance on the trade-off between privacy protection and control performance; First of all, this trade-off problem is expressed as an optimization problem of maximizing privacy protection as much as possible under the requirement of a certain control performance loss; P1 wherein , , is a predefined constant that tells the cloud that the observation matrix cannot deviate too far from the true value, here considering linear perturbations; The client uses a sparse matrix to linearly transform the innovation sequence to reduce the computational burden; in strict sense, the number of non-zero elements in the matrix is expressed by 0-norm, but since the solution of 0-norm is NP-Hard, the sparsity of the matrix is expressed by -norm.

6. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 5, wherein, Also comprise: Step five: for the solution of the optimization problem in step four, first derive the accurate expressions of the privacy index and the control performance loss; The privacy index satisfies the following Lyapunov equation: wherein indicates the innovation sequence of the system at time k covariance matrix The quadratic cost function and the privacy index satisfy the following equation: wherein ; In the infinite time domain linear quadratic control system, the control performance loss and the privacy index satisfy wherein ; In the scalar system, after the explicit expression of the privacy index and the control performance loss is known, the optimization problem in step four is solved directly; the solution of the optimization problem is the linear transformation matrix and the disturbance of the observation matrix ; The optimal target is ; wherein , are the local client and cloud steady-state prior state estimation covariances, respectively.

7. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 6, wherein, Also comprise: Step six: in a multi-dimensional system, it is difficult to directly solve the optimization problem in step four, because in a multi-dimensional system, the Lyapunov equation satisfied by the privacy index has no analytical solution; According to step five, under the given upper bound of system control performance loss, there are multiple pairs of linear transformation matrix and observation matrix disturbance solutions, and further exploration is needed to find the relationship between the two; In order to save computing resources, the sparsity of the linear transformation matrix is taken as the objective function of the optimization problem among all feasible solutions; By scaling, the optimization problem is transformed, and the trade-off between control performance loss and privacy index is transformed into the sparsity problem of the linear transformation matrix, and the problem is transformed into the collaborative design of system model disturbance and linear transformation under the premise of a certain control performance loss; P2 Further integrate and transform the restriction conditions in the optimization problem, and the linear transformation matrix satisfies the following restriction condition wherein , , , , represent the largest singular value of ; represent the largest eigenvalue of , represent the smallest eigenvalue of , represent the largest eigenvalue of ; The optimization problem in step four is transformed into the sparsity problem of the linear transformation matrix: P3 Because of its good convexity, it is directly solved using the solving tool.

8. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 7, wherein, Also comprise: Introduce model parameter disturbance into the privacy protection method, and protect privacy according to the asymmetry of model knowledge between the local client and the cloud; To achieve privacy protection against cloud-side inference, system model information perturbation is introduced. Existing privacy protection methods are understood from the perspective of system information asymmetry, introducing false noise covariance, introducing system model perturbation, and broadening the collaborative design of privacy protection methods. Under the condition of bottom-layer model information asymmetry, the trade-off between system performance loss and privacy index is transformed into the sparsity of linear transformation matrix. In step four, a privacy protection algorithm for cloud-based linear quadratic control systems under model perturbation is designed. The communication interaction between the local and the cloud is the innovation sequence derived from the observation information. Considering the connectivity of the system structure, the observation matrix in the system model parameters is perturbed.

9. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 8, wherein, Also includes: Under the condition of model knowledge asymmetry, a linear transformation method is designed to jointly design the sparse transformation of the innovation sequence transmitted by the client, the bottom-layer model perturbation, and the upper-layer sparse transformation. In step six, wherein, is an observation matrix, is a disturbance observation matrix, is a disturbance coefficient, satisfying , is a predefined constant for limiting the disturbance range of the observation matrix, the linear transformation method is applied to the control system privacy protection upper layer strategy, the privacy and performance trade-off problem in the control system is converted into an optimization problem of solving the sparsity of the matrix, and the system calculation amount is reduced.

10. The method for privacy preservation of model-based perturbed linear quadratic control systems of claim 9, wherein, Also includes: The privacy index is defined, and the deviation of the cloud's estimation of the system state from the true state estimation is taken as the privacy measure, which is more suitable for the control performance of the networked control system. The error-based measure quantifies the error made by the cloud in estimating the system state. Because calculating these measures requires information about the true results, only the local client can obtain them, in steps three and five, Because the estimation error of the cloud can be directly linked to the control performance loss of the system, the error-based measure is more suitable for networked control systems.

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