Trusted model predictive control method and device based on homomorphic encryption

Abstract

The application discloses a kind of homomorphism encryption trusted model predictive control method and device, the method includes: according to constraint linear discrete dynamic system model and reset dynamic output feedback controller model, construct the model predictive control optimization problem considering controller state reset and convert it into the optimization problem of minimizing performance index upper limit, further obtain the optimization problem under the optimization condition of reset dynamic model predictive control, and further obtain the overall optimization problem of reset dynamic model predictive control;Based on overall optimization problem, obtain dynamic model predictive controller parameter;Based on fixed-point rational number architecture quantization dynamic model predictive controller parameter;In the case where the system is stable and bounded after quantization, obtain stable quantization dynamic model predictive controller;The encryption of quantization dynamic model predictive controller is realized using homomorphism encryption.The application solves the security and privacy control problem of state-unobservable constraint control system by obtaining the encrypted dynamic model predictive controller.

Description

Technical Field

[0001] This invention relates to the field of privacy and security technology, and in particular to a semi-homomorphic encrypted trusted model prediction control method, apparatus, electronic device, and computer-readable storage medium. Background Technology

[0002] The rapid development of the Internet of Things (IoT) and cloud computing technologies has accelerated the application of Smart Cyber-Physical Systems (CPS) in various fields, such as industrial automation and intelligent transportation. However, the widespread adoption of these technologies has brought significant challenges, particularly in terms of data privacy and system security. Secure communication protocols can reduce the risk of data interception during transmission. However, they do not completely eliminate vulnerabilities associated with cloud storage and servers. Sensitive data can still be exposed to malicious attackers or misused by third-party service providers. Therefore, there is an increasing need for advanced security mechanisms to ensure the confidentiality and integrity of data throughout its entire lifecycle, including during computation.

[0003] Homomorphic encryption demonstrates significant promise for achieving cloud security and privacy in computing. Therefore, by employing homomorphic encryption, secure and private control assessments can be performed remotely without sharing sensitive data. Previous research on encrypted controllers based on homomorphic encryption largely focused on the encrypted implementation of static controllers, neglecting the physical constraints of the control system. Model predictive control (MPC) has become one of the most widely adopted control paradigms due to its advantages in optimization and system constraint handling. Current encrypted MPC methods rely on the state of the controlled object, but in practical applications, the state is often unobservable. Summary of the Invention

[0004] To address the security and privacy control issues of constraint control systems with unpredictable states, this invention provides a semi-homomorphic encrypted trusted model predictive control method, apparatus, electronic device, and computer-readable storage medium.

[0005] The first objective of this invention is to provide a trusted model prediction control method for semi-homomorphic encryption.

[0006] The second objective of this invention is to provide a trusted model prediction control device with semi-homomorphic encryption.

[0007] A third objective of this invention is to provide an electronic device.

[0008] A fourth objective of this invention is to provide a computer-readable storage medium.

[0009] The first objective of this invention can be achieved by adopting the following technical solution:

[0010] A trusted model prediction control method for semi-homomorphic encryption, the method comprising:

[0011] Based on the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model, a model predictive control optimization problem considering controller state reset is constructed.

[0012] The optimization problem of model predictive control is transformed into an optimization problem of minimizing the upper bound of the performance index; based on the optimization problem of minimizing the upper bound of the performance index, the optimization problem of reset dynamic model predictive control under the optimization conditions is obtained; based on the optimization problem under the optimization conditions, the overall optimization problem of reset dynamic model predictive control is obtained.

[0013] The overall optimization problem based on reset dynamic model predictive control is solved by obtaining the parameters of the dynamic model predictive controller offline based on the given initial state.

[0014] The parameters of the dynamic model predictive controller are quantized based on the fixed-point rational number architecture; a stable quantized dynamic model predictive controller is obtained when the quantized system is stable and bounded.

[0015] Without causing overflow in the quantized dynamic model predictive controller, semi-homomorphic encryption is used to encrypt the quantized dynamic model predictive controller to protect data privacy and system security.

[0016] Furthermore, the step of constructing a model predictive control optimization problem considering controller state reset based on the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model includes:

[0017] Based on the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model, an augmented state space model is constructed.

[0018] Based on the augmented state-space model, performance index functions for the system's measured output and control input are defined, and a model predictive control optimization problem considering controller state reset is constructed.

[0019] Furthermore, the construction of the augmented state-space model based on the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model includes:

[0020] The constrained linear discrete dynamic system model is as follows:

[0021]

[0022] In the formula, and These represent the system state, control input, and output at time k, respectively. A represents the system state at time k+1; p B p and C pAll are parameters of the state-space equations;

[0023] The control inputs and system state are constrained as follows: |φx p |≤χ;wherein, And there are h∈{1,2,…,n u}, This represents the constraint values ​​for each component of the control input; χ = [χ1, χ2, ..., χ g ] Τ χ j >0, j∈{1,2,…,g}, χ j These represent the constraint values ​​of the components related to the system state. g represents the number of constraint components related to the system state, n x The dimension representing the system state;

[0024] To address the issue of controller states overflowing the encrypted space due to iteration, a dynamic output feedback controller model is reset, as follows:

[0025]

[0026] u p (k)=C c x c (k)+D c y p (k)

[0027] In the formula, and These represent the state, input, and output of the reset dynamic output feedback controller at time k, respectively. Indicates the state of the reset dynamic output feedback controller at time k+1; A c B c C c D c These are the controller parameters to be determined;

[0028] The constructed augmented state-space model is as follows:

[0029]

[0030] in:

[0031]

[0032] In the formula, This represents the state of the augmented system at time k+1. This represents the state of the augmented system at time k;

[0033] Furthermore, the performance index function is:

[0034]

[0035] In the formula, and Both are symmetric weight matrices. Indicates the reset time; i≥0, and They represent in Predict future measurement outputs and control inputs in real time;

[0036] The model predictive control optimization problem considering controller state reset is as follows:

[0037]

[0038] st

[0039]

[0040] In the formula, and These represent the augmentation system at the reset time. Predicted and time The value, and These represent the current reset time. of The value and the current time Predicted Moment The value, Indicates the dynamic system at the reset time Predicted Time x p The value, φ represents the constraint value of the control input, φ represents the matrix acting on the system state, and χ represents the constraint value related to the system state.

[0041] Furthermore, the optimization problem of model predictive control is transformed into an optimization problem of minimizing the upper bound of the performance index; based on the optimization problem of minimizing the upper bound of the performance index, the optimization problem under the condition of resetting dynamic model predictive control is obtained, including:

[0042] Consider quadratic functions in Represents a symmetric positive definite matrix;

[0043] Suppose that when i∈{jT,jT+1,…,jT+T-2}, j∈{0,1,…}, The following performance constraints must be met:

[0044]

[0045] Assumption It satisfies the following exponential stability constraints:

[0046]

[0047] When i∈{(j+1)T}, j∈{0,1,…}, i.e. at the reset time, assume there exists a number κ that satisfies the following inequality:

[0048]

[0049] In the formula, κ∈[1,∞) and must satisfy κ(α) 2 ) T-1 ∈(0,1)

[0050] There exists a number λ > 0 such that the following expression holds:

[0051]

[0052] Combining (1-2), (1-3), and (1-4), when i∈{(j+1)T}, j∈{0,1,…}, we have:

[0053]

[0054] Summing up formulas (1-1) and (1-5) from i = 0 to ∞, we have... or Then we get:

[0055]

[0056] Where, ψ=κ(α) 2 ) T-1

[0057] Therefore, the upper bound of the performance index is:

[0058]

[0059] in,

[0060] The model predictive control optimization problem can then be expressed as an optimization problem that minimizes the upper bound of the performance index:

[0061]

[0062] st

[0063]

[0064]

[0065] Furthermore, the optimization problem under the condition of resetting the dynamic model predictive control is obtained as follows:

[0066]

[0067] subject to

[0068]

[0069] Furthermore, the optimization problem based on the optimal conditions yields the overall optimization problem for resetting the dynamic model predictive control, including:

[0070] Based on the optimization problem under the optimal conditions, variable substitution yields a solvable linear matrix inequality optimization problem;

[0071] Given that the current augmented state is within the invariant set, the overall optimization problem for resetting the dynamic model predictive control is obtained based on the solvable linear matrix inequality optimization problem.

[0072] Furthermore, the optimization problem based on the optimal conditions, through variable substitution, yields a solvable linear matrix inequality optimization problem, including:

[0073] Symmetric positive definite matrix Its inverse matrix is ​​divided into blocks as follows:

[0074]

[0075] The optimization problem under optimal conditions is transformed into a linear matrix inequality optimization problem by the following variable substitution:

[0076]

[0077] In the formula, For the replaced variable, Representing n respectively u and n x A unit vector of dimension;

[0078] Through variable substitution, the dynamic model predicts the controller parameterized as follows:

[0079]

[0080] Furthermore, the condition for the quantization dynamic model predictive controller to prevent overflow is:

[0081] and

[0082]

[0083] In the formula, This represents the fixed-point rational number architecture, where a represents the total number of bits, b represents the number of decimal places; p and q represent the total number of bits and the number of decimal places, respectively, for a stable and bounded quantized dynamic model predictive controller; n y Indicates the dimension of the system output; n c This represents the dimension by which the dynamic model predicts the controller state.

[0084] Furthermore, the parameters of the dynamic model predictive controller based on the fixed-point rational number architecture are quantized; under the condition that the quantized system is stable and bounded, a stable quantized dynamic model predictive controller is obtained, including:

[0085] Based on a fixed-point rational number architecture, the parameters of the predictive controller and the measurement output of the dynamic model are quantized.

[0086] Based on the quantized parameters of the dynamic system under stable and bounded conditions, a stable quantized dynamic model predictive controller is obtained.

[0087] The second objective of this invention can be achieved by adopting the following technical solution:

[0088] A trusted model prediction control device for semi-homomorphic encryption, the device comprising:

[0089] The optimization problem construction module is used to construct a model predictive control optimization problem that considers controller state reset based on a constrained linear discrete dynamic system model and a reset dynamic output feedback controller model.

[0090] The overall optimization problem construction module is used to transform the model predictive control optimization problem into an optimization problem that minimizes the upper bound of the performance index; based on the optimization problem that minimizes the upper bound of the performance index, the optimization problem under the optimal conditions of resetting dynamic model predictive control is obtained; based on the optimization problem under the optimal conditions, the overall optimization problem of resetting dynamic model predictive control is obtained.

[0091] The parameter generation module is used to obtain the parameters of the dynamic model predictive controller offline based on the given initial state for the overall optimization problem of reset dynamic model predictive control.

[0092] The quantization module is used to quantize the parameters of the dynamic model predictive controller based on the fixed-point rational number architecture; under the condition that the system is stable and bounded after quantization, a stable quantized dynamic model predictive controller is obtained.

[0093] The encryption module is used to encrypt the predictive controller of the quantized dynamic model using semi-homomorphic encryption to protect data privacy and system security without causing overflow in the quantized dynamic controller.

[0094] The third objective of this invention can be achieved by adopting the following technical solution:

[0095] An electronic device includes a processor and a memory for storing a processor-executable program, wherein when the processor executes the program stored in the memory, it implements the aforementioned semi-homomorphic encrypted trusted model predictive control method.

[0096] The fourth objective of this invention can be achieved by adopting the following technical solution:

[0097] A computer-readable storage medium storing a program that, when executed by a processor, implements the aforementioned semi-homomorphic encrypted trusted model predictive control method.

[0098] The present invention has the following advantages over the prior art:

[0099] This invention employs a reset dynamic output feedback controller model to construct a model predictive control optimization problem that considers controller state reset, ensuring the encrypted dynamic model predictive controller operates normally in the infinite time domain while effectively handling system constraints. Based on the constructed optimization problem, an optimization problem minimizing the upper bound of the performance index is established, which facilitates its transformation into a solvable optimization problem. By constructing a global optimization problem for reset dynamic model predictive control, it is beneficial to use existing linear matrix inequality solving tools to obtain the optimal solution. Furthermore, conditions are established to prevent encrypted data overflow, and based on semi-homomorphic encryption technology, an encrypted dynamic model predictive controller is obtained, protecting the privacy of system private data and system security. Attached Figure Description

[0100] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0101] Figure 1 This is a control block diagram of the trusted model predictive control method for semi-homomorphic encryption according to Embodiment 1 of the present invention.

[0102] Figure 2 This is a flowchart of the trusted model prediction control method for semi-homomorphic encryption according to Embodiment 1 of the present invention.

[0103] Figure 3 This is a diagram showing the controller state and the state norm of the unstable intermittent chemical reactor in the encryption control system of Embodiment 1 of the present invention.

[0104] Figure 4This is a diagram showing the output of the unstable intermittent chemical reactor in the encryption control system of Embodiment 1 of the present invention.

[0105] Figure 5 This is an encrypted output diagram of the unstable intermittent chemical reactor of the encrypted control system in Embodiment 1 of the present invention.

[0106] Figure 6 This is a control input diagram for the unstable intermittent chemical reactor in the encryption control system of Embodiment 1 of the present invention.

[0107] Figure 7 This is the encryption control input diagram for the unstable intermittent chemical reactor in Embodiment 1 of the present invention.

[0108] Figure 8 This is a comparison diagram of the state norms of the unstable intermittent chemical reactor under non-reset and reset conditions in the encryption control system of Embodiment 1 of the present invention.

[0109] Figure 9 This is a structural block diagram of the semi-homomorphic encryption trusted model prediction control device of Embodiment 2 of the present invention.

[0110] Figure 10 This is a structural block diagram of the electronic device according to Embodiment 3 of the present invention. Detailed Implementation

[0111] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be understood that the specific embodiments described are merely used to explain this application and are not intended to limit this application.

[0112] Example 1:

[0113] like Figure 1 , 2 As shown, this embodiment provides a semi-homomorphic encrypted trusted model predictive control method, using an unstable batch chemical reactor under a network control architecture as an example. The method includes the following steps:

[0114] S101. Define the performance index function based on the augmented state-space model constructed from the constrained linear discrete dynamic system and the reset dynamic output feedback controller model, and construct the model predictive control optimization problem considering controller state reset.

[0115] Unstable batch chemical reactors, as follows:

[0116]

[0117] In the formula, and These represent the system state, control input, and output at time k, respectively. A represents the system state at time k+1; p B p and C p These are all parameters of the state-space equations.

[0118] In this embodiment, A p B p and C p The values ​​are respectively:

[0119]

[0120] Control inputs and system states are subject to the following constraints:

[0121]

[0122] |φx p |≤χ

[0123] in, And there are h∈{1,2,…,n u}; χ j >0, j∈{1,2,…,g},

[0124] In this embodiment, the system is subject to the following input constraints:

[0125] To address the issue of controller states overflowing the encrypted space due to iteration, a dynamic output feedback controller model is reset, as follows:

[0126]

[0127] In the formula, and These represent the state, input, and output of the reset dynamic output feedback controller at time k, respectively. Indicates the state of the reset dynamic output feedback controller at time k+1; A c B c C c D c These are the controller parameters to be determined.

[0128] The constructed augmented state-space model is as follows:

[0129]

[0130] In the formula, This represents the state of the augmented system at time k.

[0131] The infinite time-domain performance index function for the system's measurement output and control input is defined as follows:

[0132]

[0133] In the formula, It is a symmetric weight matrix. Indicates the reset time. Indicates in Predict future measurement outputs in real time. Indicates in Predict future control inputs in all times.

[0134] In this embodiment,

[0135] The model predictive control optimization problem considering controller state reset is constructed as follows:

[0136]

[0137] st

[0138]

[0139] S102. Based on the model predictive control optimization problem, the optimization problem under the optimization conditions of the reset dynamic model predictive control is obtained; based on the optimization problem under the optimization conditions, the overall optimization problem of the reset dynamic model predictive control is obtained.

[0140] Further, step S102 includes:

[0141] (1) Based on the model predictive control optimization problem, the optimization problem under the optimization condition of resetting dynamic model predictive control is obtained.

[0142] Consider a quadratic function in Suppose that when i∈{jT,jT+1,…,jT+T-2}, j∈{0,1,…}, The following performance constraints must be met:

[0143]

[0144] Assumption It satisfies the following exponential stability constraints:

[0145]

[0146] When i∈{(j+1)T}, j∈{0,1,…}, i.e. at the reset time, assume there exists a number κ that satisfies the following inequality:

[0147]

[0148] Where κ∈[1,∞), and must satisfy κ(α) 2 ) T-1 ∈(0,1).

[0149] Therefore, there exists a number λ > 0 such that the following equation holds.

[0150]

[0151] Combining (6), (7), and (8), when i∈{(j+1)T}, j∈{0,1,…}, we have:

[0152]

[0153] Summing the performance index constraint (5) and the above equation from i = 0 to ∞, we have: or Then we can obtain:

[0154]

[0155] After sorting, we can obtain:

[0156]

[0157] Where, ψ=κ(α) 2 ) T-1 .

[0158] Therefore, the upper bound of the performance index can be obtained:

[0159]

[0160] in,

[0161] The optimization problem can be further represented as an optimization problem that minimizes the upper bound of the performance metric:

[0162]

[0163] Furthermore, the following optimization problem is obtained under the condition of resetting dynamic model predictive control:

[0164]

[0165] subject to

[0166]

[0167] (2) Based on the optimization problem under the optimal conditions, variable substitution is performed to obtain a solvable linear matrix inequality optimization problem.

[0168] Solving the optimization problem (12) under the condition of resetting dynamic model predictive control is challenging because the matrix variable A c B c C c D c and All of them are non-linear.

[0169] Symmetric positive definite matrix Its inverse matrix can be divided into blocks as follows:

[0170]

[0171] By substituting the following variables:

[0172]

[0173] The following linear matrix inequality optimization problem can be obtained:

[0174]

[0175] st

[0176]

[0177]

[0178] (3) Under the condition that the current augmented state is in the invariant set, the overall optimization problem of the dynamic model predictive control is obtained by solving the linear matrix inequality optimization problem.

[0179] Since the current state of the system is not measurable, it is necessary to remove (13-2) and provide conditions to ensure that the current augmented state remains within the invariant set in order to solve the optimization problem. Assume... in make As for the parameters to be selected, condition (13-2) can be transformed into:

[0180]

[0181] Since the optimization is performed at reset time, it includes... Then (14) can be simplified to:

[0182]

[0183] again If we ensure that the current state is within the invariant set, then equation (15) can be further expressed as:

[0184]

[0185] Before optimizing the issue at the next reset time, let:

[0186]

[0187] This can guarantee in express time The optimal value.

[0188] Next, to further reduce the conservatism, we can obtain the following from the optimization problem:

[0189]

[0190] Depend on Then there is Then in At that moment, Then there is

[0191] Furthermore, we can obtain:

[0192]

[0193] The overall optimization problem for resetting dynamic model predictive control is then expressed as:

[0194]

[0195] Through variable substitution relationships, the dynamic model predicts the controller parameterization as follows:

[0196]

[0197] The complete expression for the overall optimization problem of resetting dynamic model predictive control is:

[0198]

[0199] st

[0200]

[0201]

[0202] This embodiment derives the conditions for ensuring that the current augmented state remains within the invariant set through a synthesis method, thereby obtaining the overall optimization problem of resetting the dynamic model predictive control. This is beneficial for obtaining the optimal solution using existing linear matrix inequality solving tools.

[0203] S103. The overall optimization problem based on reset dynamic model predictive control, obtaining the dynamic model predictive controller parameters offline according to the given initial state.

[0204] Given an initial error, satisfy And given the parameter θ > 0, α∈(0,1), κ∈[1,∞), λ∈(0,∞), and the reset time T satisfy κ(α) 2 ) T-1 ∈(0,1), solve the overall optimization problem (19), and obtain the dynamic model predictive controller parameters A according to (20). c B c C c D c .

[0205] Given the initial state x, the optimization problem (19) in S102 is given. p (0) = [-6.83, -5.18, -4.05, -3.12] T x c (0) = [0,0,0,0] T , κ=12500, λ=1.2, T=30,

[0206] Solving the optimization problem (5), the parameters of the dynamic model predictive controller can be obtained:

[0207]

[0208] C c =[6.6375 -10.8148 9.3195 -11.9025], D c = [-15.6187 9.9179]

[0209] S104. Quantize the parameters and measurement output of the dynamic model predictive controller based on the fixed-point rational number architecture; under the condition that the quantized system is stable and bounded, a stable quantized dynamic model predictive controller is obtained.

[0210] The framework for fixed-point rational numbers is defined as follows:

[0211]

[0212] Based on the continuity of eigenvalues, there exists Make For all and It remains stable and satisfies the constraints, where A c Bc C c D c This represents the quantized dynamic model predictor parameters. For any... have but Quantification as Quantization definition The dynamic model predictive controller parameter A will be obtained. c B c C c D c According to the following mapping relationship:

[0213]

[0214] Mapping to the set of fixed-point rational numbers Get A c B c C c D c .

[0215] At the same time, it is also necessary to quantify the output y. p (k), quantized as if The quantization dynamic model predictive controller is then:

[0216]

[0217] This ensures that the closed-loop system is stable and that the system output is bounded, and for some δ > 0, we have:

[0218] in

[0219] when At that time, according to the mapping relationship:

[0220]

[0221] Stable A can be obtained c B c C c D c In addition, according to When p > 37, the quantization system output is obtained. Bounded.

[0222] S105. Without overflowing the quantization dynamic controller, use semi-homomorphic encryption to encrypt the quantization dynamic controller to protect data privacy and system security.

[0223] To apply Paillier semi-homomorphic encryption, it is necessary to ensure and u p (k) Only if there is no overflow within the reset interval T can the correct control quantity be obtained through decryption. For the quantized dynamic model predictive controller (21), if and Then overflow will not occur.

[0224] Before applying Paillier semi-homomorphic encryption, the variables need to be mapped to the non-negative integer field, then we have:

[0225]

[0226] In the formula, This represents the variable in the corresponding non-negative integer field. This mapping is necessary because Paillier homomorphic encryption only works in finite non-negative integer rings. Therefore, the quantization-reset dynamic controller (21) can be further represented as a controller defined in the non-negative integer field:

[0227]

[0228] Therefore, Paillier homomorphic encryption can be applied to implement the controller (22) in the positive integer field to ensure privacy-preserving control. First, a suitable public key κ must be selected. p satisfy To obtain plaintext space Ensure that the encrypted data does not overflow; then, acquire the measurement output at the sensor of the controlled object, and obtain the encrypted measurement output through quantization and non-negative integer mapping. in The result is a random number. Therefore, the encrypted dynamic controller takes the following form:

[0229]

[0230] In the formula, the operator This means for all Represents the ciphertext space; operator ◇ represents for all and Represents plaintext space.

[0231] At each sampling time k, the encrypted dynamic controller transmits the encrypted control quantity to the actuator of the controlled object to perform a decryption operation and obtain a non-negative integer field:

[0232]

[0233] In the formula, l(s)=(s-1) / κ p υ is the private key, ζ = υ -1 modκ p .

[0234] Then add control variables to the controlled object:

[0235]

[0236] In the formula, Indicates when hour, on the contrary,

[0237] To apply Paillier semi-homomorphic encryption, it is necessary to ensure x c (k) and u p (k) Only if there is no overflow within the reset interval T can the correct control quantity be obtained through decryption. For the quantized dynamic model predictive controller (21), if and Then overflow will not occur.

[0238] Before applying Paillier homomorphic encryption, the variables need to be mapped to a field of non-negative integers, which means:

[0239]

[0240] in,

[0241] Further expressed as a controller defined in the non-negative integer field:

[0242]

[0243] A suitable public key must be selected. p satisfy To ensure that the encrypted data does not overflow, and for security reasons, a 2048-bit key is chosen for encryption.

[0244] The measurement output is obtained at the system's sensor end, and after quantization and non-negative integer mapping, an encrypted measurement output is obtained. The encrypted dynamic model predictive controller then takes the following form:

[0245]

[0246] At each sampling time k, the encrypted dynamic model predictive controller transmits the encrypted control quantity to the actuator of the controlled object to perform a decryption operation and obtain the non-negative integer field. Then apply control variables to the controlled object.

[0247] Figure 3 The norm curves for the dynamic model predicting the controller state and the batch chemical reactor state show that the dynamic model predicts the controller state to reset to 0 every T=30, and the system remains stable. Figure 4 and Figure 6 The output and control input curves of the batch chemical reactor are shown below. Figure 6 It can be seen that the control inputs satisfy the constraints; Figure 5 and Figure 7 The figures show the encrypted output and encrypted control input curves of the batch chemical reactor, respectively. As can be seen from the figures, the encrypted data information is random and the actual data of the system cannot be distinguished from the encrypted data, thus protecting the security of sensitive data in the system. Figure 8 The norm curves of the batch chemical reactor state under non-reset and reset conditions of the encryption control system show that, without resetting the controller state, the encrypted data overflows the ciphertext space due to the accumulation of quantization factors, which in turn causes control errors and makes the batch chemical reactor unstable. However, by resetting, the batch chemical reactor can operate stably in the infinite time domain.

[0248] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium.

[0249] It should be noted that although the method operations of the above embodiments are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the order of execution of the described steps may be changed. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0250] Example 2:

[0251] like Figure 9 As shown, this embodiment provides a semi-homomorphic encrypted trusted model prediction and control device. This device includes an optimization problem construction module 901, a global optimization problem construction module 902, a parameter generation module 903, a quantization module 904, and an encryption module 905, wherein:

[0252] The optimization problem construction module 901 is used to construct a model predictive control optimization problem that considers controller state reset based on a constrained linear discrete dynamic system model and a reset dynamic output feedback controller model.

[0253] The overall optimization problem construction module 902 is used to transform the model predictive control optimization problem into an optimization problem that minimizes the upper bound of the performance index; based on the optimization problem that minimizes the upper bound of the performance index, the optimization problem under the optimal conditions of resetting dynamic model predictive control is obtained; based on the optimization problem under the optimal conditions, the overall optimization problem of resetting dynamic model predictive control is obtained.

[0254] The parameter generation module 903 is used to obtain the parameters of the dynamic model predictive controller offline based on the given initial state for the overall optimization problem of reset dynamic model predictive control.

[0255] The quantization module 904 is used to quantize the parameters of the dynamic model predictive controller based on the fixed-point rational number architecture; under the condition that the quantized system is stable and bounded, a stable quantized dynamic model predictive controller is obtained.

[0256] The encryption module 905 is used to encrypt the quantized dynamic model predictive controller using semi-homomorphic encryption to protect data privacy and system security without causing overflow in the quantized dynamic controller.

[0257] The specific implementation of each module in this embodiment can be found in Embodiment 1 above, and will not be repeated here. It should be noted that the device provided in this embodiment is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0258] Example 3:

[0259] This embodiment provides an electronic device, which can be a computer, such as... Figure 10 As shown, the processor 1002, memory, input device 1003, display 1004, and network interface 1005 are connected via system bus 1001. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 1006 and internal memory 1007. The non-volatile storage medium 1006 stores the operating system, computer programs, and database. The internal memory 1007 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 1002 executes the computer programs stored in the memory, it implements the semi-homomorphic encryption trusted model predictive control method of Embodiment 1 described above.

[0260] Example 4:

[0261] This embodiment provides a storage medium, which is a computer-readable storage medium, storing a computer program. When the computer program is executed by a processor, it implements the semi-homomorphic encryption trusted model prediction control method of Embodiment 1 above.

[0262] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0263] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and inventive concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A trusted model predictive control method with semi-homomorphic encryption, characterized in that, The method includes: Based on the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model, a model predictive control optimization problem considering controller state reset is constructed. The optimization problem of model predictive control is transformed into an optimization problem of minimizing the upper bound of the performance index; based on the optimization problem of minimizing the upper bound of the performance index, the optimization problem of reset dynamic model predictive control under the optimization conditions is obtained; based on the optimization problem under the optimization conditions, the overall optimization problem of reset dynamic model predictive control is obtained. The overall optimization problem based on reset dynamic model predictive control is solved by obtaining the parameters of the dynamic model predictive controller offline based on the given initial state. The parameters of the dynamic model predictive controller are quantized based on the fixed-point rational number architecture; a stable quantized dynamic model predictive controller is obtained when the quantized system is stable and bounded. Without causing overflow in the quantized dynamic model predictive controller, semi-homomorphic encryption is used to encrypt the quantized dynamic model predictive controller to protect data privacy and system security. The reset dynamic output feedback controller model is as follows: u p (k)=C c x c (k)+D c y p (k) In the formula, x c (k), y p (k) and u p (k) represents the state, input, and output of the reset dynamic output feedback controller at time k, respectively; x c (k+1) represents the state of the reset dynamic output feedback controller at time k+1; A c B c C c D c These are the controller parameters to be determined.

2. The reliable model predictive control method according to claim 1, characterized in that, The step of constructing a model predictive control optimization problem considering controller state reset based on a constrained linear discrete dynamic system model and a reset dynamic output feedback controller model includes: Based on the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model, an augmented state space model is constructed. Based on the augmented state-space model, performance index functions for the system's measured output and control input are defined, and a model predictive control optimization problem considering controller state reset is constructed.

3. The reliable model predictive control method according to claim 2, characterized in that, The process of constructing an augmented state-space model based on a constrained linear discrete dynamic system model and a reset dynamic output feedback controller model includes: The constrained linear discrete dynamic system model is as follows: In the formula, This represents the system state at time k. A represents the system state at time k+1; p B p and C p All are parameters of the state-space equations; The control inputs and system state are constrained as follows: |φx p |≤χ;wherein, h∈{1,2,…,n u }, This represents the constraint values ​​for each component of the control input, and has... χ=[χ1,χ2,…,χ g ] Τ , j∈{1,2,…,g}, χ j χ represents the constraint values ​​of each component related to the system state. j >0; g represents the number of constraint components related to the system state, n x The dimension representing the system state; The constructed augmented state-space model is as follows: in: In the formula, This represents the state of the augmented system at time k+1. This represents the state of the augmented system at time k.

4. The reliable model predictive control method according to claim 3, characterized in that, The performance index function is: In the formula, and Both are symmetric weight matrices. Indicates the reset time; i≥0, and They represent in Predict the measurement output and control input at time i in the future; The model predictive control optimization problem considering controller state reset is as follows: In the formula, and These represent the augmentation system at the reset time. Predicted and time The value, and These represent the current reset time. of The value and the current time Predicted Moment The value, Indicates the dynamic system at the reset time Predicted Time x p The value, φ represents the constraint value of the control input, φ represents the matrix acting on the system state, and χ represents the constraint value related to the system state.

5. The reliable model predictive control method according to claim 4, characterized in that, The process of transforming the model predictive control optimization problem into an optimization problem that minimizes the upper bound of the performance index; and based on the optimization problem that minimizes the upper bound of the performance index, obtaining the optimization problem under the condition of resetting dynamic model predictive control, including: Consider quadratic functions in Represents a symmetric positive definite matrix; Suppose that when i∈{nT,nT+1,…,nT+T-2}, n∈{0,1,…}, The following performance constraints must be met: Assumption It satisfies the following exponential stability constraints: When i∈{(n+1)T}, i.e. at the reset time, assume there exists a number κ that satisfies the following inequality: In the formula, κ∈[1,∞) and must satisfy κ(α) 2 ) T-1 ∈(0,1) There exists a number λ > 0 such that the following expression holds: Combining (1-2), (1-3), and (1-4), when i∈{(n+1)T}, we have: Summing up formulas (1-1) and (1-5) from i = 0 to ∞, we have... or Then we get: Where, ψ=κ(α 2 ) T-1 Therefore, the upper bound of the performance index is: in, The model predictive control optimization problem can then be expressed as an optimization problem that minimizes the upper bound of the performance index: The optimization problem under the condition of resetting dynamic model predictive control is:

6. The reliable model predictive control method according to claim 3, characterized in that, The optimization problem based on the optimal conditions yields the overall optimization problem for resetting dynamic model predictive control, including: Based on the optimization problem under the optimal conditions, variable substitution yields a solvable linear matrix inequality optimization problem; Given that the current augmented state is within the invariant set, the overall optimization problem for resetting the dynamic model predictive control is obtained based on the solvable linear matrix inequality optimization problem.

7. The reliable model predictive control method according to claim 6, characterized in that, The optimization problem based on the optimal conditions, through variable substitution, yields a solvable linear matrix inequality optimization problem, including: Symmetric positive definite matrix Its inverse matrix is ​​divided into blocks as follows: The optimization problem under optimal conditions is transformed into a linear matrix inequality optimization problem by the following variable substitution: In the formula, For the replaced variable, Representing n respectively u and n x A unit vector of dimension; Through variable substitution, the dynamic model predicts the controller parameterized as follows:

8. The reliable model predictive control method according to claim 3, characterized in that, The condition for preventing overflow in the quantized dynamic model predictive controller is: and In the formula, This represents the fixed-point rational number architecture, where a represents the total number of bits, b represents the number of decimal places; p and q represent the total number of bits and the number of decimal places, respectively, for a stable and bounded quantized dynamic model predictive controller; n y Indicates the dimension of the system output; n c This represents the dimension by which the dynamic model predicts the controller state.

9. The reliable model predictive control method according to any one of claims 2 to 8, characterized in that, The parameters of the quantized dynamic model predictive controller based on the fixed-point rational number architecture are obtained; under the condition that the quantized system is stable and bounded, a stable quantized dynamic model predictive controller is obtained, including: Based on a fixed-point rational number architecture, the parameters of the predictive controller and the measurement output of the dynamic model are quantized. Based on the quantized parameters of the dynamic system under stable and bounded conditions, a stable quantized dynamic model predictive controller is obtained.

10. A trusted model prediction control device with semi-homomorphic encryption, characterized in that, The device includes: The optimization problem construction module is used to construct a model predictive control optimization problem that considers controller state reset based on a constrained linear discrete dynamic system model and a reset dynamic output feedback controller model. The overall optimization problem construction module is used to transform the model predictive control optimization problem into an optimization problem that minimizes the upper bound of the performance index; based on the optimization problem that minimizes the upper bound of the performance index, the optimization problem under the optimal conditions of resetting dynamic model predictive control is obtained; based on the optimization problem under the optimal conditions, the overall optimization problem of resetting dynamic model predictive control is obtained. The parameter generation module is used to obtain the parameters of the dynamic model predictive controller offline based on the given initial state for the overall optimization problem of reset dynamic model predictive control. The quantization module is used to quantize the parameters of the dynamic model predictive controller based on the fixed-point rational number architecture; under the condition that the system is stable and bounded after quantization, a stable quantized dynamic model predictive controller is obtained. The encryption module is used to encrypt the predictive controller of the quantized dynamic model using semi-homomorphic encryption to protect data privacy and system security without causing overflow in the quantized dynamic controller. The reset dynamic output feedback controller model is as follows: u p (k)=C c x c (k)+D c y p (k) In the formula, x c (k), y p (k) and u p (k) represents the state, input, and output of the reset dynamic output feedback controller at time k, respectively; x c (k+1) represents the state of the reset dynamic output feedback controller at time k+1; A c B c C c D c These are the controller parameters to be determined.

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