Semi-homomorphic encryption trusted model prediction control method and device

Abstract

The invention discloses a semi-homomorphic encryption trusted model prediction control method and device, and the method comprises the steps: carrying out the feedback of a controller model according to a constraint linear discrete dynamic system model and a reset dynamic output model; constructing a model predictive control optimization problem considering controller state reset and converting the model predictive control optimization problem into an optimization problem of minimizing the upper bound of a performance index, thereby obtaining an optimization problem under an optimization condition of reset dynamic model predictive control, and further obtaining an overall optimization problem of the reset dynamic model predictive control; based on the overall optimization problem, dynamic model prediction controller parameters are obtained; quantizing a dynamic model prediction controller parameter based on a fixed-point rational number architecture; under the condition that the quantized system is stable and bounded, a stable quantized dynamic model prediction controller is obtained; and realizing encryption of the quantitative dynamic model prediction controller by utilizing semi-homomorphic encryption. According to the method, the security privacy control problem of the constraint control system with the unmeasurable state is solved by obtaining the encrypted dynamic model predictive controller.

Description

Technical Field

[0001] The present invention relates to the technical field of privacy security, and particularly to a trusted model predictive control method, device, electronic device and computer-readable storage medium for homomorphic encryption. Background Art

[0002] The rapid development of Internet of Things (IoT) and cloud computing technologies has accelerated the development of cyber-physical systems (CPS) in various fields, such as industrial automation and intelligent transportation. However, the widespread adoption of these technologies has brought huge challenges, especially 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 the vulnerabilities associated with cloud storage and the server side. Sensitive data may 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 life cycle, including during computing.

[0003] Homomorphic encryption shows important prospects for achieving cloud security and privacy in computing. Therefore, by adopting homomorphic encryption, secure and private control evaluation can be remotely performed without sharing sensitive data. Most previous studies on encrypted controllers based on homomorphic encryption focused on the encrypted implementation of static controllers without considering 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 all rely on the state of the controlled object, but in practical applications, the state is often unobservable. Summary of the Invention

[0004] To solve the security and privacy control problem of a constrained control system with unmeasurable states, the present invention provides a trusted model predictive control method, device, electronic device and computer-readable storage medium for homomorphic encryption.

[0005] The first object of the present invention is to provide a trusted model predictive control method for homomorphic encryption.

[0006] The second object of the present invention is to provide a trusted model predictive control device for homomorphic encryption.

[0007] The third object of the present invention is to provide an electronic device.

[0008] The fourth object of the present invention is to provide a computer-readable storage medium.

[0009] The first object of the present invention can be achieved by adopting the following technical solutions:

[0010] A trusted model predictive control method for homomorphic encryption, the method comprising:

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

[0012] Transform the model predictive control optimization problem into an optimization problem of minimizing the upper bound of the performance index; According to the optimization problem of minimizing the upper bound of the performance index, obtain the optimization problem under the optimal conditions of the reset dynamic model predictive control; Based on the optimization problem under the optimal conditions, obtain the overall optimization problem of the reset dynamic model predictive control;

[0013] Based on the overall optimization problem of the reset dynamic model predictive control, obtain the dynamic model predictive controller parameters offline according to the given initial state;

[0014] Quantize the dynamic model predictive controller parameters based on the fixed-point rational number architecture; When the system is stable and bounded after quantization, obtain a stable quantized dynamic model predictive controller;

[0015] When the quantized dynamic model predictive controller does not overflow, use homomorphic encryption to encrypt the quantized dynamic model predictive controller to protect data privacy and system security.

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

[0017] Construct an augmented state space model according to the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model;

[0018] According to the augmented state space model, define the performance index function of the measured output and control input of the system, and construct a model predictive control optimization problem considering the reset of the controller state.

[0019] Furthermore, the constructing of the augmented state space model according to 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:

[0021]

[0022] where and represent the system state, control input, and output at time k respectively, represents the system state at time k + 1; A p , B p and C pare all the parameters of the state-space equation;

[0023] The control input and the system state are subject to the following constraints: φx p | ≤ χ; where, and represents the constraint values of the components of the control input; χ = [χ 1 , χ 2 , …, χ g Τ χ j > 0, h ∈ {1, 2, …, g}, χ j represents 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 represents the dimension of the system state;

[0024] To address the problem that the controller state overflows the encryption space due to iteration, a reset dynamic output feedback controller model is adopted as follows:

[0025]

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

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

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

[0029]

[0030] Where:

[0031]

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

[0033] Furthermore, the performance index function is:​

[0034]

[0035] where θ > 0 and are both symmetric weight matrices, represents the reset time; i ≥ 0, and respectively represent the predicted future measurement output and control input at time;

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

[0037]

[0038] s.t.

[0039]

[0040] where and respectively represent the predicted at the reset time and time values of and respectively represent the at the current reset time value of and the predicted at the current time value of represents the predicted at the reset time time x p value of 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 model predictive control optimization problem is transformed into an optimization problem of minimizing the upper bound of the performance index; according to the optimization problem of minimizing the upper bound of the performance index, the optimization problem under the optimal conditions of the reset dynamic model predictive control is obtained, including:

[0042] Considering the quadratic function where represents a symmetric positive definite matrix;

[0043] Assume that when i ∈ {jT, jT + 1, …, jT + T - 2}, j ∈ {0, 1, …}, satisfies the following performance index constraints:

[0044]

[0045] Suppose the following exponential stability constraints are satisfied:

[0046]

[0047] When \(i\in\{(j + 1)T\}\), \(j\in\{0,1,\cdots\}\), i.e., the reset time, suppose there exists a number \(\kappa\) satisfying the following inequality:

[0048]

[0049] where \(\kappa\in[1,\infty)\) and \(\kappa(\alpha 2 ) T-1 \(\in(0,1)\)

[0050] There exists a number \(\lambda>0\) such that the following holds:

[0051]

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

[0053]

[0054] Summing up formula (1 - 1) and (1 - 5) from \(i = 0\) to \(\infty\), and having or Then we get:

[0055]

[0056] where \(\psi=\kappa(\alpha 2 ) T-1

[0057] Furthermore, the upper bound of the performance index is obtained as:

[0058]

[0059] where

[0060] Then the model predictive control optimization problem is expressed as the optimization problem of minimizing the upper bound of the performance index:

[0061]

[0062]

[0063] Furthermore, the optimization problem under the optimal conditions of the reset dynamic model predictive control is obtained as:

[0064]

[0065] Furthermore, the overall optimization problem of reset dynamic model predictive control obtained from the optimization problem under the optimal conditions includes:

[0066] Based on the optimization problem under the optimal conditions, variable substitution is performed to obtain a solvable linear matrix inequality optimization problem;

[0067] Under the condition of ensuring that the current augmented state is within the invariant set, the overall optimization problem of reset dynamic model predictive control is obtained according to the solvable linear matrix inequality optimization problem.

[0068] Furthermore, the variable substitution based on the optimization problem under the optimal conditions to obtain a solvable linear matrix inequality optimization problem includes:

[0069] Symmetric positive definite matrix And its inverse matrix are partitioned as follows:

[0070]

[0071] Through the following variable substitution for the optimization problem under the optimal conditions, a linear matrix inequality optimization problem is obtained:

[0072]

[0073] Wherein, Is the variable after substitution, Respectively represent n u And n x Dimensional unit vectors;

[0074] Through variable substitution, the parameters of the dynamic model predictive controller are parameterized as:

[0075]

[0076] Furthermore, the condition for the quantization dynamic model predictive controller not to overflow is:

[0077]

[0078] Wherein, Represents a fixed-point rational number architecture, where a represents the total number of bits, and b represents the number of fractional bits; p and q respectively represent the total number of bits and the number of fractional bits for the quantization dynamic model predictive controller to be stable and the system to be bounded; n y Represents the dimension of the system output; n c Represents the dimension of the state of the dynamic model predictive controller.

[0079] Furthermore, the parameters of the quantized dynamic model predictive controller are based on a fixed-point rational number architecture; in the case where the system is stable and bounded after quantization, a stable quantized dynamic model predictive controller is obtained, including:

[0080] Based on the fixed-point rational number architecture, quantize the parameters of the dynamic model predictive controller and the measured output;

[0081] According to the quantization parameters in the case where the quantized dynamic system is stable and bounded, obtain a stable quantized dynamic model predictive controller.

[0082] The second object of the present invention can be achieved by adopting the following technical solutions:

[0083] A trusted model predictive control device with homomorphic encryption, the device includes:

[0084] An optimization problem construction module, configured to construct a model predictive control optimization problem considering controller state reset according to the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model;

[0085] An overall optimization problem construction module, configured to transform the model predictive control optimization problem into an optimization problem of minimizing the upper bound of the performance index; according to the optimization problem of minimizing the upper bound of the performance index, obtain the optimization problem under the optimal conditions of the reset dynamic model predictive control; based on the optimization problem under the optimal conditions, obtain the overall optimization problem of the reset dynamic model predictive control;

[0086] A parameter generation module, configured to offline obtain the parameters of the dynamic model predictive controller based on the overall optimization problem of the reset dynamic model predictive control according to the given initial state;

[0087] A quantization module, configured to quantize the parameters of the dynamic model predictive controller based on the fixed-point rational number architecture; in the case where the system is stable and bounded after quantization, obtain a stable quantized dynamic model predictive controller;

[0088] An encryption module, configured to, in the case where the quantized dynamic controller does not overflow, use homomorphic encryption to implement the encryption of the quantized dynamic model predictive controller to protect data privacy and system security.

[0089] The third object of the present invention can be achieved by adopting the following technical solutions:

[0090] An electronic device, including a processor and a memory for storing a program executable by the processor, when the processor executes the program stored in the memory, implementing the above-mentioned trusted model predictive control method with homomorphic encryption.

[0091] The fourth object of the present invention can be achieved by adopting the following technical solutions:

[0092] A computer-readable storage medium stores a program which, when executed by a processor, implements the above-mentioned trusted model predictive control method for homomorphic encryption.

[0093] The present invention has the following beneficial effects compared with the prior art:

[0094] By adopting a reset dynamic output feedback controller model, the present invention constructs an optimal problem of model predictive control considering the reset of the controller state, ensuring the normal operation of the encrypted dynamic model predictive controller in the infinite time domain and effectively handling system constraints; according to the constructed optimal problem, an optimal problem of minimizing the upper bound of the performance index is established, which is conducive to being converted into a solvable optimal problem; by constructing the overall optimal problem of reset dynamic model predictive control, it is conducive to using existing linear matrix inequality solving tools to obtain the optimal solution; establishing the condition for non-overflow of encrypted data and obtaining an encrypted dynamic model predictive controller based on homomorphic encryption technology protects the privacy of system private data and system security. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0096] Figure 1 It is the control block diagram of the trusted model predictive control method for homomorphic encryption in Embodiment 1 of the present invention.

[0097] Figure 2 It is the flowchart of the trusted model predictive control method for homomorphic encryption in Embodiment 1 of the present invention.

[0098] Figure 3 It is the norm diagram of the controller state and the unstable batch chemical reactor state of the encrypted control system in Embodiment 1 of the present invention.

[0099] Figure 4 It is the output diagram of the unstable batch chemical reactor of the encrypted control system in Embodiment 1 of the present invention.

[0100] Figure 5 It is the encrypted output diagram of the unstable batch chemical reactor of the encrypted control system in Embodiment 1 of the present invention.

[0101] Figure 6 It is the control input diagram of the unstable batch chemical reactor of the encrypted control system in Embodiment 1 of the present invention.

[0102] Figure 7 Encryption control input diagram of the unstable batch chemical reactor of the encryption control system according to Embodiment 1 of the present invention.

[0103] Figure 8 Comparison diagram of the state norms of the unstable batch chemical reactor with non-reset and reset of the encryption control system according to Embodiment 1 of the present invention.

[0104] Figure 9 Structure block diagram of the trusted model predictive control device with semi-homomorphic encryption according to Embodiment 2 of the present invention.

[0105] Figure 10 Structure block diagram of the electronic device according to Embodiment 3 of the present invention. Detailed implementation manners

[0106] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention. It should be understood that the specific embodiments described are only for explaining the present application and are not used to limit the present application.

[0107] Embodiment 1:

[0108] As Figure 1 、 2 shown, this embodiment provides a trusted model predictive control method with semi-homomorphic encryption, taking an unstable batch chemical reactor under a network control architecture as an example for illustration. The method includes the following steps:

[0109] S101. Define a performance index function according to the augmented state space model constructed by the constrained linear discrete dynamic system and the reset dynamic output feedback controller model, and construct a model predictive control optimization problem considering controller state reset.

[0110] For the unstable batch chemical reactor, as follows:

[0111]

[0112] In the formula, and respectively represent the system state, control input and output at time k, represents the system state at time k + 1; A p , B p and C p are all state space equation parameters.

[0113] In this embodiment, A p , B p and C p are respectively valued as:

[0114]

[0115] The control input and system state are subject to the following constraints:

[0116]

[0117] φx p | ≤ χ

[0118] where, and there is χ = [χ 1 , χ 2 , …, χ g Τ χ j > 0, h ∈ {1, 2, …, g},

[0119] In this embodiment, the system is subject to the input constraint as

[0120] To address the problem that the controller state overflows the encryption space due to iteration, a reset dynamic output feedback controller model is adopted as follows:

[0121]

[0122] In the formula, and respectively represent the state, input, and output of the reset dynamic output feedback controller at time k; represents the state of the reset dynamic output feedback controller at time k + 1; A c , B c , C c , D c are the controller parameters to be determined.

[0123] The constructed augmented state - space model is as follows:

[0124]

[0125] In the formula, represents the state of the augmented system at time k,

[0126] The infinite - time - domain performance index function regarding the measurement output and control input of the system is defined as follows:

[0127] ​

[0128] where θ > 0, is a symmetric weight matrix, represents the reset time, represents at time predicting the future measurement output, represents at time predicting the future control input.

[0129] In this embodiment, θ = diag(10, 10),

[0130] Construct the model predictive control optimization problem considering the controller state reset as follows:

[0131]

[0132] S102. According to the model predictive control optimization problem, obtain the optimization problem under the optimization conditions of the reset dynamic model predictive control; based on the optimization problem under the optimization conditions, obtain the overall optimization problem of the reset dynamic model predictive control.

[0133] Furthermore, step S102 includes:

[0134] (1) According to the model predictive control optimization problem, obtain the optimization problem under the optimization conditions of the reset dynamic model predictive control.

[0135] Consider a quadratic function where Assume that when i ∈ {jT, jT + 1, …, jT + T - 2}, j ∈ {0, 1, …}, satisfies the following performance index constraints:

[0136]

[0137] Assume satisfies the following exponential stability constraints:

[0138]

[0139] When i ∈ {(j + 1)T}, j ∈ {0, 1, …}, that is, the reset time, assume that there exists a number κ satisfying the following inequality:

[0140]

[0141] where κ ∈ [1, ∞), and it is required to satisfy κ(α 2 ) T-1 ∈ (0, 1).

[0142] Therefore, there exists a number λ > 0 such that the following equation holds

[0143]

[0144] Combining (6), (7), and (8), when \(i\in\{(j + 1)T\}\), \(j\in\{0, 1,\cdots\}\), we have:

[0145]

[0146] Summing up the performance index constraint (5) and the above equation from \(i = 0\) to \(\infty\), and we have Or Then we can obtain:

[0147]

[0148] After rearrangement, we can get:

[0149]

[0150] where \(\psi=\kappa(\alpha 2 ) T-1 .

[0151] Therefore, we can obtain the upper bound of the performance index:

[0152]

[0153] where,

[0154] The optimization problem can be further expressed as an optimization problem of minimizing the upper bound of the performance index:

[0155]

[0156] Furthermore, we obtain the following optimization problem under the optimal conditions of the reset dynamic model predictive control:

[0157]

[0158] (2) Based on the optimization problem under the optimal conditions, variable substitution is performed to obtain a solvable linear matrix inequality optimization problem.

[0159] Solving the optimization problem (12) under the optimal conditions of the reset dynamic model predictive control is challenging because the matrix variables \(A c , B c , C c , D c and are all non - linear.

[0160] The symmetric positive - definite matrix and its inverse matrix can be partitioned as follows:

[0161]

[0162] By means of the following variable substitution:

[0163]

[0164] The following linear matrix inequality optimization problem can be obtained:

[0165]

[0166]

[0167] (3) Under the condition of ensuring that the current augmented state is within the invariant set, the overall optimization problem of the reset dynamic model predictive control is obtained according to the solvable linear matrix inequality optimization problem.

[0168] Since the current state of the system is not measurable, (13 - 2) needs to be removed, and the condition for ensuring that the current augmented state remains within the invariant set is given to solve the optimization problem. Assume where Let be the parameters to be selected, and the condition (13 - 2) can be transformed into:

[0169]

[0170] Since the optimization is performed at the reset moment, where there is Then (14) can be simplified to:

[0171]

[0172] Also To ensure that the current state is within the invariant set, Equation (15) can be further expressed as:

[0173]

[0174] Before the optimization problem at the next reset moment, let:

[0175]

[0176] Then it can be ensured that where represents the moment the optimal value.

[0177] Next, to further reduce the conservatism, from the optimization problem, we have:

[0178]

[0179] From There is Then at moment, let There is

[0180] Furthermore, it can be obtained that:

[0181]

[0182] Resetting the overall optimization problem of dynamic model predictive control is expressed as:

[0183]

[0184] Through the variable substitution relationship, the parameters of the dynamic model predictive controller are parameterized as:

[0185]

[0186] That is, the complete expression of the overall optimization problem of resetting the dynamic model predictive control is:

[0187]

[0188]

[0189] In this embodiment, through a comprehensive method, the conditions for ensuring that the current augmented state remains within the invariant set are derived, and the overall optimization problem of resetting the dynamic model predictive control is obtained, which is beneficial to using existing linear matrix inequality solving tools to obtain the optimal solution.

[0190] S103. Based on the overall optimization problem of resetting the dynamic model predictive control, obtain the parameters of the dynamic model predictive controller offline according to the given initial state.

[0191] Given that the initial error satisfies 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 parameters A c , B c , C c , D c .

[0192] From the optimization problem (19) in S102, given the initial state x 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,

[0193] Solving the optimization problem (5), the parameters of the dynamic model predictive controller can be obtained:

[0194]

[0195] C c = [6.6375 -10.8148 9.3195 -11.9025], D c = [-15.6187 9.9179]

[0196] S104. Quantize the parameters of the dynamic model predictive controller and the measurement output based on the fixed-point rational number architecture; when the quantized system is stable and bounded, a stable quantized dynamic model predictive controller is obtained.

[0197] Define the fixed-point rational number architecture as follows:

[0198]

[0199] According to the continuity of the eigenvalues, there exists such that For all and is still stable and satisfies the constraint requirements, where A c , B c , C c , D c represent the parameters of the quantized dynamic model predictive controller. For any and there is Then The quantization of The quantization of The parameters A c , B c , C c , D c are mapped according to the following mapping relationship:

[0200]

[0201] Mapped to the fixed-point rational number set to obtain A c , B c , C c , D c .

[0202] At the same time, it is also necessary to quantize the measurement output y p (k), quantized to If then the quantized dynamic model predictive controller is:

[0203]

[0204] such that the closed-loop system is stable and the system output is bounded. For some δ > 0, there is

[0205] where

[0206] When at that time, according to the mapping relationship:

[0207]

[0208] a stable A c , B c , C c , D c can be obtained. In addition, according to it can be obtained that when p > 37, the quantized system output is bounded.

[0209] S105. Without overflow occurring in the quantized dynamic controller, use homomorphic encryption to encrypt the quantized dynamic controller to protect data privacy and system security.

[0210] To apply Paillier homomorphic encryption, it is necessary to ensure and u p (k) do not overflow within the reset interval T, so that the correct control quantity can be obtained through decryption. For the quantized dynamic model predictive controller (21), if and then no overflow will occur.

[0211] Before applying Paillier homomorphic encryption, the variables need to be mapped to the non-negative integer domain, then there is

[0212]

[0213] In the formula, represents the variable in the corresponding non-negative integer domain. This mapping is necessary because Paillier homomorphic encryption only works in the finite non-negative integer ring. Therefore, the quantized reset dynamic controller (21) can be further expressed as a controller defined in the non-negative integer domain:

[0214]

[0215] Therefore, the Paillier homomorphic encryption can be applied to implement the controller (22) in the positive integer domain to ensure privacy-preserving control. First, a suitable public key κ must be selected p Satisfy To obtain the plaintext space Ensure that the encrypted data does not overflow; then the measured output is obtained at the sensor end of the controlled object, and the encrypted measured output is obtained through quantization and non-negative integer mapping Where Is a random number. Then the encrypted dynamic controller is expressed as follows:

[0216]

[0217] In the formula, the operator Represents for all Represents the ciphertext space; the operator ◇ represents for all And Represents the plaintext space.

[0218] At each sampling time k, the encrypted dynamic controller transmits the encrypted control quantity to the actuator end of the controlled object to perform the decryption operation to obtain the non-negative integer domain:

[0219]

[0220] In the formula, l(s)=(s - 1) / κ p , υ is the private key,

[0221] Then apply the control quantity to the controlled object:

[0222]

[0223] In the formula, Represents when When, Conversely,

[0224] In order to apply the Paillier semi-homomorphic encryption, it is necessary to ensure that x c (k) and u p (k) do not overflow within the reset interval T, so that the correct control quantity can be obtained through decryption. For the quantized dynamic model predictive controller (21), if And Then there will be no overflow.

[0225] Before applying the Paillier homomorphic encryption, the variables need to be mapped to the non-negative integer domain, then there is:

[0226]

[0227] Among them,

[0228] It is further expressed that the controller defined in the non - negative integer domain is:

[0229]

[0230] A suitable public key κ must be selected p Satisfying Ensure that the encrypted data will not overflow, and for security, a 2048 - bit key is selected for encryption.

[0231] At the sensor end of the system, the measurement output is obtained, and through quantization and non - negative integer mapping, the encrypted measurement output is obtained Then the expression form of the encrypted dynamic model predictive controller is as follows:

[0232]

[0233] At each sampling time k, the encrypted dynamic model predictive controller transmits the encrypted control quantity to the actuator end of the controlled object to perform decryption operation to obtain the non - negative integer domain Then apply the control quantity to the controlled object

[0234] Figure 3 It is the norm curve of the dynamic model predictive controller state and the intermittent chemical reactor state. It can be seen that the dynamic model predictive controller state will reset to 0 every T = 30, and the system is still stable; Figure 4 And Figure 6 Are the output and control input curves of the intermittent chemical reactor respectively. From Figure 6 It can be seen that the control input satisfies the constraint conditions; Figure 5 And Figure 7 Are the encrypted output and encrypted control input curves of the intermittent chemical reactor respectively. From the figure, it can be seen that the encrypted data information shows randomness, and the actual data of the system cannot be distinguished from the encrypted data, thus protecting the security of the sensitive data in the system; Figure 8 It is the norm curve of the intermittent chemical reactor state in the case of non - reset and reset of the encrypted control system. It can be seen that, due to not resetting the controller state, the encrypted data overflows the ciphertext space due to the accumulation of quantization factors, which in turn causes control action errors, making the intermittent chemical reactor unable to be stably controlled. While using reset, the intermittent chemical reactor can work stably in the infinite time domain.

[0235] Those skilled in the art can understand that all or part of the steps in the methods of the above embodiments can be completed by instructing relevant hardware through a program, and the corresponding program can be stored in a computer-readable storage medium.

[0236] It should be noted that although the method operations of the above embodiments are described in a specific order in the drawings, this does not require or imply that these operations must be performed in that specific order, or that all the shown operations must be performed to achieve the desired result. On the contrary, the depicted steps can be executed in a changed order. Additionally or alternatively, certain steps can be omitted, multiple steps can be combined into one step for execution, and / or one step can be decomposed into multiple steps for execution.

[0237] Embodiment 2:

[0238] As Figure 9 shown, this embodiment provides a trustworthy model predictive control device for homomorphic encryption. The device includes an optimization problem construction module 901, an overall optimization problem construction module 902, a parameter generation module 903, a quantization module 904, and an encryption module 905, where:

[0239] The optimization problem construction module 901 is used to construct a model predictive control optimization problem considering controller state reset according to the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model;

[0240] The overall optimization problem construction module 902 is used to transform the model predictive control optimization problem into an optimization problem of minimizing the upper bound of the performance index; according to the optimization problem of minimizing the upper bound of the performance index, obtain the optimization problem under the optimal conditions of the reset dynamic model predictive control; based on the optimization problem under the optimal conditions, obtain the overall optimization problem of the reset dynamic model predictive control;

[0241] The parameter generation module 903 is used to obtain the dynamic model predictive controller parameters offline based on the overall optimization problem of the reset dynamic model predictive control according to the given initial state;

[0242] The quantization module 904 is used to quantize the dynamic model predictive controller parameters based on a fixed-point rational number architecture; when the system is stable and bounded after quantization, obtain a stable quantized dynamic model predictive controller;

[0243] The encryption module 905 is used to use homomorphic encryption to encrypt the quantized dynamic model predictive controller to protect data privacy and system security when the quantized dynamic controller does not overflow.

[0244] For the specific implementation of each module in this embodiment, reference can be made to Embodiment 1 above, which will not be elaborated here one by one. It should be noted that the device provided in this embodiment is only illustrated by the above division of each functional module. In practical applications, the above functions can be assigned to different functional modules according to needs, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0245] Embodiment 3:

[0246] This embodiment provides an electronic device, which can be a computer. As Figure 10 shown, it includes a processor 1002, a memory, an input device 1003, a display 1004, and a network interface 1005 connected through a system bus 1001. The processor is used to provide computing and control capabilities. The memory includes a non-volatile storage medium 1006 and an internal memory 1007. The non-volatile storage medium 1006 stores an operating system, a computer program, and a database. The internal memory 1007 provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. When the processor 1002 executes the computer program stored in the memory, it implements the semi-homomorphic encryption-based trusted model predictive control method of Embodiment 1 above.

[0247] Embodiment 4:

[0248] This embodiment provides a storage medium, which is a computer-readable storage medium and stores a computer program. When the computer program is executed by a processor, it implements the semi-homomorphic encryption-based trusted model predictive control method of Embodiment 1 above.

[0249] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two. A 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 of the above. More specific examples of a computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0250] As described above, it is only a preferred embodiment of the present invention patent, but the protection scope of the present invention patent is not limited thereto. Any person skilled in the art within the scope disclosed by the present invention patent, according to the technical solution and inventive concept of the present invention patent, makes equivalent substitutions or changes, which all belong to the protection scope of the present invention patent.

Claims

1. A semi-homomorphic encrypted trusted model predictive control method, characterized in that: The method comprises: 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 the 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 optimal conditions of resetting the dynamic model predictive control is obtained; based on the optimization problem under the optimal conditions, the overall optimization problem of resetting the dynamic model predictive control is obtained; Based on the overall optimization problem of resetting the dynamic model predictive control, the dynamic model predictive controller parameters are obtained offline according to the given initial state; Quantizing the parameters of the dynamic model predictive controller based on a fixed-point rational number architecture; obtaining a stable quantized dynamic model predictive controller when the system is stable and bounded after quantization; When the quantized dynamic model predictive controller does not overflow, semi-homomorphic encryption is used to encrypt the quantized dynamic model predictive controller to protect data privacy and system security.

2. The credible model predictive control method according to claim 1, characterized in that: The method 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: According to the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model, an augmented state space model is constructed; According to the augmented state space model, the performance index function of the system's measured output and control input is defined, and a model predictive control optimization problem considering controller state reset is constructed.

3. The credible model predictive control method according to claim 2, characterized in that: The augmented state space model is constructed according to the constrained linear discrete dynamic system model and the reset dynamic output feedback controller model, including: The constrained linear discrete dynamic system model is: In the formula, and They 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 They are all state space equation parameters; The control inputs and system states are constrained as: φx p |≤χ; where And there is h∈{1,2,…,n u }, Represents the constraint value of each component of the control input; h∈{1,2,…,g},χ j represents the constraint value of each component related to the system state, g represents the number of constraint components related to the system state, n x The dimension representing the state of the system; In order to deal with the problem that the controller state overflows the encryption space due to iteration, a reset dynamic output feedback controller model is adopted as follows: u p (k)=C c x c (k)+D c y p (k) In the formula, and denote the state, input and output of the reset dynamic output feedback controller at time k respectively; A represents the state of the reset dynamic output feedback controller at time k+1; c , B c , C c , D c is the controller parameter to be requested; The constructed augmented state space model is as follows: in: In the formula, represents the state of the augmented system at time k+1, represents the state of the augmented system at time k.

4. The credible model predictive control method according to claim 3, characterized in that: The performance indicator function is: Where θ>0 and are all symmetric weight matrices, Indicates the reset time; i≥0, and Respectively expressed in Always predict future measurement outputs and control inputs; The model predictive control optimization problem considering controller state reset is: In the formula, and They represent the augmented system at the reset time Predicted and time The value of and Respectively represent the current reset time of The value and current time Predicted Moment The value of Indicates that the dynamic system is at the reset time Predicted Time x p The value of 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 credible model predictive control method according to claim 4, characterized in that: The optimization problem of model predictive control is converted into the optimization problem of minimizing the upper bound of the performance index; according to the optimization problem of minimizing the upper bound of the performance index, the optimization problem under the optimal conditions of resetting the dynamic model predictive control is obtained, including: Consider the quadratic function in represents a symmetric positive definite matrix; Assume that when i∈{jT,jT+1,…,jT+T-2}, j∈{0,1,…}, The following performance constraints are met: Assumptions The following exponential stability constraints are satisfied: When i∈{(j+1)T},j∈{0,1,…}, i.e., at the reset time, assume that 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 holds: Combining (1-2), (1-3) and (1-4), when i∈{(j+1)T},j∈{0,1,…}, we have: Add up formulas (1-1) and (1-5) from i=0 to ∞, and we have or Then we get: Where, ψ=κ(α 2 ) T-1 Then the upper bound of the performance index is obtained as: in, Then the model predictive control optimization problem is expressed as the optimization problem of minimizing the upper bound of the performance index: The optimization problem under the optimal conditions of resetting the dynamic model predictive control is:

6. The credible model predictive control method according to claim 3, characterized in that: The optimization problem based on the optimization condition is used to obtain the overall optimization problem of resetting the dynamic model predictive control, including: Based on the optimization problem under the optimization condition, variable substitution is performed to obtain a solvable linear matrix inequality optimization problem; Under the condition that the current augmented state is within the invariant set, the overall optimization problem of the reset dynamic model predictive control is obtained according to the solvable linear matrix inequality optimization problem.

7. The credible model predictive control method according to claim 6, characterized in that: The optimization problem based on the optimization condition is subjected to variable substitution to obtain a solvable linear matrix inequality optimization problem, including: Symmetric positive definite matrix And its inverse matrix is ​​divided into blocks as follows: The optimization problem under the optimal conditions is replaced by the following variables to obtain the linear matrix inequality optimization problem: In the formula, is the variable after substitution, Respectively represent n u and n x -dimensional unit vector; By variable substitution, the dynamic model predictive controller is parameterized as:

8. The credible model predictive control method according to claim 3, characterized in that: The condition for the quantized dynamic model predictive controller to not overflow is: In the formula, represents the fixed-point rational number architecture, where a represents the total number of bits and b represents the number of decimal places; p and q represent the total number of bits and the number of decimal places for the quantized dynamic model predictive controller to be stable and the system to be bounded, respectively; n y Indicates the dimension of the system output; n c The dimensionality of the dynamic model predicting the controller state.

9. The credible model predictive control method according to any one of claims 2 to 8, characterized in that: The method of quantizing the parameters of the dynamic model predictive controller based on the fixed-point rational number architecture and obtaining a stable quantized dynamic model predictive controller when the system is stable and bounded after quantization includes: Quantize dynamic model predictive controller parameters and measured outputs based on fixed-point rational number architecture; According to the stability of the dynamic system after quantization and the quantization parameters under bounded conditions, a stable quantized dynamic model predictive controller is obtained.

10. A semi-homomorphic encrypted trusted model predictive control device, characterized in that: The device comprises: An optimization problem construction module is used to construct a model predictive control optimization problem considering controller state reset according to a constrained linear discrete dynamic system model and a reset dynamic output feedback controller model; The overall optimization problem building module is used to transform the model predictive control optimization problem into the optimization problem of minimizing the upper bound of the performance index; according to the optimization problem of minimizing the upper bound of the performance index, the optimization problem under the optimal conditions of resetting the dynamic model predictive control is obtained; based on the optimization problem under the optimal conditions, the overall optimization problem of resetting the dynamic model predictive control is obtained; A parameter generation module, for obtaining the parameters of the dynamic model predictive controller offline according to a given initial state based on resetting the overall optimization problem of the dynamic model predictive control; A quantization module is used to quantize the parameters of the dynamic model predictive controller based on a fixed-point rational number architecture; when the system is stable and bounded after quantization, a stable quantized dynamic model predictive controller is obtained; The encryption module is used to implement encryption of the quantized dynamic model predictive controller using semi-homomorphic encryption to protect data privacy and system security without overflow of the quantized dynamic controller.

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