Design Method of Safety Controller for Networked Control Systems

Abstract

The present invention discloses a method for designing a security controller for a networked control system, comprising: establishing a T-S fuzzy networked control system (NCSs) resistant to DoS attacks; formulating data compression rules under limited channel bandwidth; introducing an adaptive learning I ETC under the supervision of small-batch machine learning; and formulating a performance error evaluation mechanism to assess the performance error of the control system. The present invention ensures efficient network resource allocation, robustness, and reliability.

Description

Technical Field

[0001] The present invention relates to the technical field of networked control systems, in particular to a design method for a safety controller of a networked control system. Background Art

[0002] In the 1970s, with the emergence of distributed control systems (DCSs), network technology was introduced into industrial control systems [1]. Prior to this, control systems used point-to-point connections to connect digital control (DDC) sensors and actuators to the same computer [2]. However, due to cost constraints and the centralized distribution of computer systems, DDC technology had difficulty handling single-point failure problems in the system. With the introduction of network technology in DCS, control tasks were distributed to field control systems (FCSs) controlled by multiple small computers, greatly improving the efficiency and reliability of the control system [3]. After more than 20 years of development of FCS technology, existing network technology no longer meets the needs of large-scale centralized and decentralized control. The introduction of Ethernet technology has increased the transmission efficiency of FCS and enabled control systems to evolve from automation to industrial automation. Therefore, networked control systems (NCSs) combine the high reliability and flexibility of FCS with higher transmission efficiency [4].

[0003] Many studies have focused on various issues related to NCSs. For example, some authors proposed different underlying network scheduling protocols to address the latency problem in NCSs and analyzed their stability, as shown in [5]. In [6], another study proposed a new method to ensure the mean square stability of NCSs and designed a controller to achieve this goal. In [7], nonlinear problems in NCSs were studied and stability criteria based on linear NCSs were proposed. In addition, in [8], the authors addressed the problem of limited communication resources in NCSs by solving the finite-time consensus tracking control problem of nonlinear networked multi-agent systems. In addition, [9] proposed a resilient fuzzy stability criterion to improve the stability and reliability of TS fuzzy NCSs. However, there is still a research gap in solving the network congestion and communication security problems caused by DoS attacks on NCSs.

[0004] With the rapid development of information technology, NCSs have developed into integrated automated information systems supported by hardware, software, and network technologies. Since the network is the core technology of NCSs, ensuring the security of the communication network has become a key research topic

[10] . It is crucial to establish a security control strategy for NCSs to ensure optimal system performance [11-15],

[26] . In

[11] , a security control method for NCSs was proposed to mitigate DoS attacks. In addition, an event-triggered control method was proposed in

[12] to analyze the stability of NCSs under normal operation and DoS attacks. Cheng et al. explored the relationship between periodic DoS attacks and decay rate in

[13] . In contrast, the problem of stability control and stable data transmission rate conditions for NCSs under DoS attacks was studied in

[14] . In order to better analyze the performance of NCSs under DoS attacks, Cai et al. proposed a novel event-triggered communication scheme in

[15] . However, after a network attack, NCSs may experience performance degradation and system errors. Therefore, estimating the performance error of the system has become a key research topic, which is of great significance for designing security protection mechanisms for future NCSs

[16] ,

[17] .

[0005] In order to build NCSs, it is necessary to fully utilize system integration technology, build the initial Internet-internet-internet network mechanism, and realize distributed NCSs. Autonomous vehicles (AVs) based on NCSs are key technologies for intelligent transportation systems, integrating various high-tech solutions. A large amount of research has been done on AVs, including planning functions of expert systems, computer vision, autonomous navigation, and advanced parallel processing technologies

[18] ,

[19] ,

[22] . AVs are able to make independent judgments and plans, accept natural language tasks, formulate methods for executing tasks, and continuously revise plans. As a design concept, AVs are able to complete certain tasks through complex terrain

[20] . The combination of NCSs and AV control systems is of great significance because NCSs are a new control technology that relies on the Internet after industrial control systems

[21] . Therefore, research in this field is very important.

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[0017]

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[0018]

[13] Z.H.Cheng,D.Yue,S.G.Shen,S.L.Hu,and L.Chen,Resilient event-triggered controller synthesis ofNCSs under periodic DoS jamming attacks,IEEETransactions on Cybernetics,vol.49,no.12,pp.4271-4281,2019.

[0019]

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[0020]

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[0021]

[16] X.Cai,K.B.Shi,K.She,S.M.Zhong,Y.C.Soh,Y.Yu,Performance errorestimation and elastic integralevent triggering mechanism design for T-Sfuzzy networked control system under DoS attacks,IEEE Transactionson FuzzySystems,vol.31,no.4,pp.1327-1339,2022.

[0022]

[17] H.C.Y.Yang,C.Peng,and Z.R.Cao,A novel memory-based schedulingprotocol for networked controlsystems under stochastic attacks and bandwidthconstraint,IEEE / CAA Journal of Automatica Sinica,vol.10,no.5,pp.1336-1339,2023.

[0023]

[18] Y.F.Ma,Z.Y.Wang,H.Yang and L.Yang,Artificial intelligenceapplications in the development ofautonomous vehicles:a survey,IEEE / CAAJournal of Automatica Sinica,vol.7,no.2,pp.315-329,2020.

[0024]

[19] Z. Lian, P. Shi, C. C. Lim, and X. Yuan, Fuzzy-model-based lateral control for networked autonomous vehicle systems under hybrid cyber-attacks, IEEE Transactions on Cybernetics, vol. 53, no. 4, pp. 2600-2609, 2022.

[0025]

[20] Y. Wu, L. F. Wang, J. Z. Zhang, and F. Li, Path following control of autonomous ground vehicle based on nonsingular terminal sliding mode and active disturbance rejection control, IEEE Transactions on Vehicular Technology, vol. 68, no. 7, pp. 6379-6390, 2019.

[0026]

[21] A. Eskandarian, C. X. Wu, and C. Y. Sun, Research advances and challenges of autonomous and connected ground vehicles, IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 2, pp. 683-711, 2021.

[0027]

[22] Z. H. Peng, D. Wang, T. S. Li, and M. Han, Output-feedback cooperative formation maneuvering of autonomous surface vehicles with connectivity preservation and collision avoidance, IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2527-2535, 2020. Summary of the Invention

[0028] To solve the problems existing in the prior art, the purpose of the present invention is to provide a safety controller design method for a networked control system, which ensures efficient network resource allocation, robustness and reliability.

[0029] To achieve the above object, the present invention adopts a technical solution: a method for designing a safety controller for a networked control system, comprising the following steps:

[0030] Step 1: Establish TS fuzzy networked control system NCSs under DoS attack;

[0031] Step 2: Formulate data compression rules under limited channel bandwidth;

[0032] Step 3: Introduce IETC for adaptive learning under mini-batch machine learning supervision;

[0033] Step 4: Develop a performance error evaluation mechanism to evaluate the control system performance error.

[0034] As a further improvement of the present invention, the step 1 is specifically as follows:

[0035] Consider TS fuzzy NCSs with the following fuzzy rules:

[0036] Rule i: If λ 1t yes and λ mt yes So:

[0037]

[0038] Among them, x t is the state variable of the system, represents the external disturbance; the output of the system is z t , the control input signal is u t ; A i ,B i ,C i and E i is the parameter matrix;

[0039] Fuzzy membership function δ i (μ t ) is defined as follows:

[0040]

[0041] Among them, Q i m (λ t ) represents λ mt exist In addition, for all t≥0, the condition and Established;

[0042] Standard fuzzy inference methods are used to transform NCSs into the following form:

[0043]

[0044] in:

[0045]

[0046]

[0047] Assume that the sampling period of the system is represented by h, and the sampling time in the time interval kh is represented by t kh In order to describe DoS attacks, a preliminary formula is provided:

[0048]

[0049] in, Indicates the time period of the Nth DoS attack, where Indicates the number of attacks; in time When the attack signal is active, The value is 1, and at time t k+1h When the attack signal enters the dormant state, The value is 0; represents the period of time without DoS attack within the Nth time interval; then, the following conditions are established:

[0050]

[0051] The trigger threshold is represented by ρ, whose value ranges from 0 to 1; the variable Indicates the current status The status of the last successful transmission Differences between; variables Defined as in Represents the last successful transmission status under DoS attack; the intensity of the attack is determined by Then, the transmission sequence is determined using the IETC condition. As shown below:

[0052]

[0053] Among them, the sampling time set of DoS attack is composed of represents, N represents the index of the attack; Indicates the active time period of the Nth DoS attack, where and t k+1h,N Respectively represent the start and end time of the attack;

[0054] Using the fuzzy center balancer, the following input control is obtained:

[0055] Rule j: If λ 1t yes and λ mt yes So:

[0056]

[0057] Then, the fuzzy controller is reformulated as follows:

[0058]

[0059] in, K j is the control gain matrix.

[0060] As a further improvement of the present invention, the step 2 is specifically as follows:

[0061] A flow compression function model is defined, denoted as T(·). The range of the flow compression function model is defined as follows:

[0062]

[0063] Define the model T(u t ) and formulate the following compression rules:

[0064] (I) If the control input signal satisfies or set up

[0065] (II) If the control input signal satisfies or set up

[0066] (III) If the control input signal satisfies or Set T(u t )=0;

[0067] (IV) If the control input signal satisfies and other situations, set The parameters and 0<θ<1, is T(u t )’s dead zone size;

[0068] After the attack, the compressed control signal value is expressed as:

[0069]

[0070] Among them, the nonlinear function H(u t ) and vector U t Satisfying 1-γ≤H(u t )≤1+γ and Using Equation (2) and Equation (9), TS fuzzy NCSs can be expressed as follows:

[0071]

[0072] As a further improvement of the present invention, the step 3 is specifically as follows:

[0073] Determine the optimal trigger threshold ρ within the specified interval θ and formulate a weakly convex optimization problem, considering the constraints of avoiding network congestion and maximizing bandwidth utilization in the presence of DoS attacks:

[0074]

[0075] Among them, the optimal trigger threshold ρ∈θ=[0,1]; the optimization target of determining ρ is represented by F, that is,

[0076] Use the mini-batch proximal gradient method to find the optimal trigger threshold ρ within a given interval θ; generate a sequence ρ that converges to the optimal threshold by iteratively solving formula (11) k+1 ; The sequence is represented as follows:

[0077]

[0078] set up is a convex function with a Lipschitz continuous gradient, is a possibly non-smooth convex function; the step size parameter is denoted by h l ; The iteration form is as follows:

[0079]

[0080] Combining the proximal operator with stochastic gradient descent, it is defined as follows:

[0081]

[0082] Among them, the random estimate of the gradient pass Get, which is defined as follows:

[0083]

[0084] Among them, the random estimate of the gradient is obtained by selecting from the set [n] = {1, 2, ..., n} the probability of q i >0 random index i selected k Calculated, and the convex function f ik Used to determine The average value of is used to calculate the gradient reference point.

[0085] As a further improvement of the present invention, in step 4, the control system performance error is evaluated based on the system performance evaluation and estimation rules of the reachable set concept, as follows:

[0086] (1) Define the following ellipsoid boundaries

[0087]

[0088] (2) The performance error estimation problem is transformed into the problem of finding an ellipsoid, as follows:

[0089]

[0090] (3) Given a real scalar If LKFsV is present t Satisfying V0=0,ω t Satisfies formula (17) and satisfies Then get

[0091] Given a τ t ∈[a,b], any matrix and satisfy Then the following inequality is satisfied:

[0092]

[0093] As a further improvement of the present invention, it also includes:

[0094] According to the new constraints to ensure the performance error estimation of the system, consider the TS fuzzy NCSs described in formula (10), where τ, γ, u min 、 and ρ are positive scalars; let Π(P) denote the boundary of the ellipsoid, assuming that there exist symmetric matrices P>0, Q>0, R, and matrices S, N1, N2 and satisfies the following LMI for all i,j=1,2,...,r:

[0095] Λ(Ξ,Y,F)<0 (18)

[0096] in:

[0097] Λ(Ξ,Y,F)=Ξ+Y+F;

[0098]

[0099]

[0100]

[0101]

[0102] As a further improvement of the present invention, it also includes:

[0103] According to the new constraints to ensure the performance error estimation of the system, consider the TS fuzzy NCSs described in formula (10), where τ, γ, u min 、 and ρ are positive scalars; let Π(P) denote the boundary of the ellipsoid, assuming that there exist symmetric matrices P>0, Q>0, R, and matrices S, N1, N2, X, Y j and satisfies the following LMI for all i,j=1,2,…,r:

[0104]

[0105] in:

[0106]

[0107]

[0108]

[0109]

[0110] e i =[0 n×(i-1)n I n×n 0 n×(9-i) ],i=1,2,...,9.

[0111] The beneficial effects of the present invention are:

[0112] This paper proposes a performance error estimation rule to assess the degradation of AV system performance under DoS attacks and introduces a data compression mechanism to alleviate the network congestion caused by such attacks. It also introduces adaptive learning-based Inter-Electronic Traffic Control (IETC) supervised by machine learning to estimate AV system errors. This IETC strategy ensures efficient network resource allocation, robustness, and reliability. The main contributions are as follows:

[0113] (1) The communication security of network-controlled AV systems is studied, and a performance error estimation rule is established to evaluate the performance degradation of AV systems under network attacks.

[0114] (2) An improved data compression mechanism is developed to optimize the allocation and use of network resources under limited bandwidth. This mechanism aims to alleviate the communication network congestion problem caused by DoS attacks.

[0115] (3) An adaptive learning I ETC strategy is proposed to ensure accurate estimation of AV system performance error under mini-batch supervision. In addition, the mathematical derivation is simplified by using more general LKFs. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 Schematic diagram of the data compression mechanism and process in Example 1 of the present invention;

[0117] Figure 2 : is a graph of the T(·) compression function in Example 1 of the present invention;

[0118] Figure 3 Schematic diagram of a performance error estimation set in Example 1 of the present invention;

[0119] Figure 4 Schematic diagram of a path-following autonomous driving vehicle model in Example 2 of the present invention;

[0120] Figure 5 This is a state trajectory diagram of the AV system under DoS attack in Example 2 of the present invention;

[0121] Figure 6 Schematic diagram of the error estimated ellipsoid boundary obtained through different compression steps in Example 2 of the present invention;

[0122] Figure 7 Performance error evaluation in Example 2 of the present invention Π(P) Ellipsoid boundary map;

[0123] Figure 8 Schematic diagram of the relationship between the ellipse edge and the system performance error estimation under different trigger thresholds in Example 2 of the present invention.

[0124] Figure 9 Schematic diagram of a path-following autonomous driving vehicle model in Example 2 of the present invention;

[0125] Figure 10 Schematic diagram of AV system control input under DoS attack in Example 2 of the present invention. DETAILED DESCRIPTION

[0126] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0127] Example 1

[0128] A safety controller design method for a networked control system, comprising:

[0129] 1. TS Fuzzy NCSs and DoS Attacks:

[0130] Consider TS fuzzy NCSs with the following fuzzy rules:

[0131] Rule i: If λ 1t yes and λ mt yes So:

[0132]

[0133] Among them, x t is the state variable of the system, represents the external disturbance. The output of the system is z t , the control input signal is u t . A i ,B i ,C i and E i is the parameter matrix.

[0134] Fuzzy membership function δ i (μ t ) can be defined as follows:

[0135]

[0136] in, Represents λ mt exist In addition, for all t≥0, the condition and Established.

[0137] Standard fuzzy inference methods are used to transform NCSs into the following form:

[0138]

[0139] in:

[0140]

[0141]

[0142] The main goal of this embodiment is to address the security challenges that arise when NCSs use the Internet to exchange information. A solution is proposed that takes into account the vulnerabilities of the TCP / IP protocol and focuses on resolving DoS attacks. Specifically, assume that the sampling period of the system is represented by h, and the sampling time within the time interval kh is represented by t kh To describe DoS attacks, this paper provides a preliminary formula below:

[0143]

[0144] Among them, the definition Indicates the time period of the Nth DoS attack, where Indicates the number of attacks. When the attack signal is active, The value is 1, and at time t k+1h When the attack signal enters the dormant state, The value is 0. In addition, Indicates the period of time during which there is no DoS attack within the Nth time interval. Then, the following conditions are established:

[0145]

[0146] The trigger threshold is represented by ρ, and its value ranges from 0 to 1. Indicates the current status The status of the last successful transmission The difference between variables Defined as in here, Represents the last successful transmission state under DoS attack. The intensity of the attack is represented by ζ, which is equal to the vector Then, the transmission sequence is determined using the IETC condition As shown below:

[0147]

[0148] Among them, the sampling time set of DoS attack is composed of represents, and N represents the index of the attack. Indicates the active time period of the Nth DoS attack, where and t k+1h,N Represent the start and end time of the attack respectively. To obtain the fuzzy controller, this embodiment uses a fuzzy center balancer, which is similar to the method described in formula (2). The following input control can be obtained:

[0149] Rule j: If λ 1tyes and λ mt yes So:

[0150]

[0151] Then, the fuzzy controller is reformulated as follows:

[0152]

[0153] in, K j is the control gain matrix.

[0154] 2. Data compression rules under limited channel bandwidth:

[0155] One way to mitigate the impact of a DoS attack on server operations is to increase data traffic within the available bandwidth. This can help relieve congestion, increase throughput, and maintain a smooth communication channel, such as Figure 1 and Figure 2 To achieve this goal, a traffic compression function model, denoted as T(·), can be used, which can effectively compress data while maintaining its quality. This approach reduces the volume of transmitted data traffic, thereby improving throughput, reducing latency, and reducing congestion.

[0156] The proposed model T(u t ) is crucial in improving the efficiency of communication networks, especially in mitigating the impact of DoS attacks. The scope of the traffic compression function model is defined as follows:

[0157]

[0158] Next, define the model T(u t ) and formulate the following compression rules:

[0159] (I) If the control input signal satisfies or set up

[0160] (II) If the control input signal satisfies or set up

[0161] (III) If the control input signal satisfies or Set T(u t )=0.

[0162] (IV) If the control input signal satisfies and other situations, set

[0163] Here, The parameters and 0<θ<1, is T(u t ) of the dead zone.

[0164] Therefore, after the attack, the compressed control signal value, as measured in formula (7), can be expressed as:

[0165]

[0166] Among them, the nonlinear function H(u t ) and vector U t Satisfying 1-γ≤H(u t )≤1+γ and Using equations (2) and (9), TS fuzzy NCSs can be expressed as follows:

[0167]

[0168] 3. IETC under Mini-Batch Machine Learning Supervision:

[0169] The optimal trigger threshold ρ is determined within a specified interval θ. The proposed method formulates a weakly convex optimization problem, considering the constraints of avoiding network congestion and maximizing bandwidth utilization in the presence of DoS attacks.

[0170]

[0171] Among them, the optimal trigger threshold ρ∈θ=[0,1]. Specifically, it is necessary to determine the optimization target of ρ represented by F, that is,

[0172] In order to find the optimal trigger threshold ρ within a given interval θ, a mini-batch proximal gradient method is used. The algorithm generates a sequence ρ that converges to the optimal threshold by iteratively solving (11) k+1 . This sequence can be represented as follows:

[0173]

[0174] set up is a convex function with a Lipschitz continuous gradient, is a convex function that may be non-smooth. The step size parameter is denoted as h l The iteration form is as follows:

[0175]

[0176] The stochastic proximal gradient method is used to accelerate convergence in large-scale computations. This method combines the proximal operator with stochastic gradient descent and is defined as follows:

[0177]

[0178] Among them, the random estimate of the gradient pass Get, which is defined as follows:

[0179]

[0180] Among them, the random estimate of the gradient is obtained by selecting from the set [n] = {1, 2, ..., n} the probability of q i >0 random index i selected k Calculated, and the convex function f ik Used to determine The average value of is the previously calculated gradient reference point.

[0181] 4. Performance error evaluation mechanism:

[0182] The impact of DoS attacks on system performance is significant and may lead to increased channel load and communication congestion. To address this issue, estimating the extent of performance degradation after an attack is crucial, which has become a new research direction in this field. Therefore, this embodiment proposes a set of system performance evaluation and estimation rules based on the concept of reachable sets (see Figure 3 By understanding these rules and their application in the system, you can better predict its performance and take appropriate measures to mitigate the impact of DoS attacks. This embodiment proposes the following steps to deal with this problem:

[0183] (1) Define the following ellipsoid boundaries

[0184]

[0185] (2) The performance error estimation problem is transformed into the problem of finding an ellipsoid, as follows:

[0186]

[0187] (3) Given a real scalar If LKFsV is present t Satisfying V0=0,ω t Satisfies (17) and satisfies Then you can get

[0188] Given a τ t ∈[a,b], any matrix and satisfy Then the following inequality is satisfied:

[0189]

[0190] 5. Main results:

[0191] This embodiment introduces the performance error estimation of nonlinear NCSs under DoS attack described in Equation (12). To achieve this goal, this embodiment proposes two theorems. Theorem 1 proposes new constraints to ensure the performance error estimation of the system, while Theorem 2 introduces the calculation of the control gain matrix K j (λ) method.

[0192] Theorem 1: Consider the TS-fuzzy NCSs described in Equation (10), where τ, γ, u min 、 and ρ are positive scalars. Let Π(P) denote the boundary of the ellipsoid. Suppose there exist symmetric matrices P>0, Q>0, R, and matrices S, N1, N2, and satisfies the following LMI for all i,j=1,2,...,r:

[0193] Λ(Ξ,Y,F)<0 (18)

[0194] Wherein, Λ(Ξ,Y,Θ), Ξ, Y, Θ and other symbols are listed in Appendix I.

[0195] Proof: See Appendix II(1).

[0196] Theorem 2: Consider the TS-fuzzy NCSs given by Equation (10), where τ, γ, u min 、 and ρ are positive scalars. Let Π(P) denote the boundary of the ellipsoid. Suppose there exist symmetric matrices P>0, Q>0, R, and matrices S, N1, N2, X, Y j and satisfies the following LMI for all i,j=1,2,…,r:

[0197]

[0198] in, and other symbols are listed in Appendix I.

[0199] Proof: Please see Appendix II(2).

[0200] Appendix I

[0201] Λ(Ξ,Y,F)=Ξ+Y+F

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] e i =[0 n×(i-1)n I n×n 0 n×(9-i) ],i=1,2,...,9

[0212] Appendix II(1)

[0213] In order to prove the stability of TS-fuzzy NCSs given by (10), LKFs are selected as follows:

[0214] V t =V t 1 +V t 2 +V t 3 (20)

[0215] in:

[0216]

[0217]

[0218]

[0219] Then, V t The time derivative of is given by:

[0220]

[0221]

[0222]

[0223] Here, we use the integral inequality of Jensen’s inequality and Lemma 1 to scale the integral terms in equations (24) and (25). Therefore, the following inequality holds:

[0224]

[0225] Then, by considering the trigger condition (5) under the machine learning algorithm, the following inequality is obtained:

[0226]

[0227] Furthermore, for system (10), there exist arbitrary matrices N1 and N2 such that the following equation holds:

[0228]

[0229] Finally, based on the analysis in formulas (22)-(29), the following inequality holds:

[0230]

[0231] When Λ(Π,Ξ,Ω)<0 holds, it means In other words, when t∈[t kh ,t k+1h ), it satisfies the performance error estimation rule, and it can be proved that x T Px≤V t ≤ 1. Therefore, the set of performance error estimates is contained in Π(P).

[0232] Appendix II(2)

[0233] The control gain matrix and other symbols in this embodiment are defined as follows:

[0234]

[0235]

[0236] Multiply (18) by X T and X to obtain LMI (19). The rest of the proof and the design process of solving the control gain matrix are the same as in Theorem 1.

[0237] Example 2

[0238] This embodiment is tested on a front-wheel drive AV with limited yaw, longitudinal, roll and pitch angles, such as Figure 4 The model was constructed based on previous studies, and important parameters were extracted and presented in Table 1.

[0239] Table 1: The parameter values ​​for the autonomous vehicle are as follows:

[0240] describe symbol Numerical unit Yaw rate γ - rad / s Yaw moment <![CDATA[I z ]]> 3000 <![CDATA[kg·m 2 <!-- 14 -->]]> Vehicle quality m 1500 kg Speed v 20 m / s Sideslip angle δ - rad Steering angle <![CDATA[δ f ]]> - rad Curve driving force <![CDATA[F f / F r ]]> - N Center distance <![CDATA[l f / l r ]]> 1.3 / 1.2 m

[0241] Then, the following expression can be used to describe the nonlinear steering force characteristics that satisfy the fuzzy rules:

[0242] Rule 1:

[0243] Rule 2:

[0244] The parameter ρ f and ρ γ is defined as and Among them C γ1 =60088, C γ2 =3455, C f1 =60712, and C f2 =4812 is selected. The state vector and control input are defined as and u t =δ f ,(u min =0.5).

[0245] The following are the definitions of the basic membership functions:

[0246]

[0247] The parameter matrix of the nonlinear NCS that satisfies two fuzzy rules can be expressed as follows:

[0248]

[0249] First, this example studies the impact of cyberattacks on the AV system during operation. In order to evaluate the performance of the AV system and estimate the error in the AV system performance after the cyberattack, two key parameters are used. Then, the maximum acceptable time delay (MAUBs) is used to estimate the communication performance of the AV system. By setting the compression index to γ ​​= 0.2 and the attack intensity to The trigger threshold is set to ρ = 0.7239, and the YALMIP toolbox in MATLAB is used to solve the LMIs in Theorem 1. The experimental results show that the performance error evaluation parameters can affect the value of MAUBs, as shown in Table 2. These findings provide a basis for further verification of the performance error estimation parameters in the future.

[0250] Table 2: MAUBs values ​​for different performance error estimation indices are as follows:

[0251]

[0252] The experimental results in Table 2 show the impact of different performance error estimation indicators on the MAUBs of AV systems. For example, when When running the experiment on a computer equipped with Intel(R) Core(TM) i7-8565UCPU@1.80GHz1.99GHz, it takes 2.14 seconds to obtain τ=2.3762. In contrast, when choosing When , the corresponding MAUBs is 1.0981 and the required time is 1.17 seconds. These results clearly show that the performance error evaluation metric can significantly affect the value of MAUBs. These findings are crucial for validating the formulation of performance error estimation parameters and defense mechanisms in future experiments.

[0253] Table 3: Performance error estimation indicators under different attack intensities as follows:

[0254]

[0255] The results presented in Table 3 show that the performance of the AV system degrades as the attack intensity increases. Specifically, when the attack intensity is set to When the performance error estimation index is 4.6674, while for The performance error estimate index is As the attack intensity increases, the estimated performance error of the AV system decreases by 37.17%. Further investigation reveals that the severity of cyberattacks has a significant impact on AV systems, and in some cases, performance degradation may become irreversible. Therefore, accurately estimating the performance error of AV systems under network communication security is crucial to ensure safe and reliable operation.

[0256] In order to better understand the impact of the attack on the AV system, this embodiment conducted another experiment to estimate the performance error caused by the attack. γ = 0.2 and ρ = 0.7239, and the performance error estimation index was calculated using MATLAB The results are shown in Table 4. The table provides the performance error estimation index values ​​for different time periods. It is observed that the performance error increases with the increase in time period, which confirms that the attack causes an increase in performance error. This experiment provides evidence that the performance error caused by the attack can be estimated and can serve as a basis for developing defense mechanisms to resist the attack. In addition, Figure 5 The running status trajectory of the system under DoS attack is drawn in Figure .

[0257] On the one hand, a data compression mechanism is developed to cope with network congestion and thus mitigate the impact of DoS attacks. Different compression steps are applied to evaluate their effectiveness. Figure 6 As shown, the error estimation ellipses obtained by different compression steps show that The most accurate error estimate is achieved when Figure 7 In [1], the boundaries of the performance error ellipse are plotted to evaluate the system's performance under varying attack intensities. The semi-major axis of the ellipsoid provides an estimate of the solution's performance error. The results show that the error increases with increasing attack intensity, highlighting the importance of developing robust solutions to DoS attacks.

[0258] Table 4: The trigger rates under machine learning supervision are as follows:

[0259] Machine Learning Process Trigger times Trigger rate Threshold ρ = 0.2134 68 72.34％ Threshold ρ = 0.3381 70 64.22％ Threshold ρ = 0.6601 79 75.24％ Threshold ρ = 0.7239 48 51.06％

[0260] On the other hand, an innovative IETC controller is proposed, which integrates a trigger controller supervised by a mini-batch machine learning algorithm to ensure the optimization of system performance and verify the accuracy of system performance error estimation. Figure 8 The relationship between the ellipse edge and the system performance error estimation under different trigger thresholds is shown. In addition, Table 4 provides the trigger times and trigger frequencies of the system under different trigger thresholds ρ. These results demonstrate the effectiveness of the proposed IETC controller in maintaining system stability and mitigating the impact of cyber attacks on AV system performance.

[0261] Applying machine learning algorithms to develop triggering mechanisms for AV systems has shown great potential for addressing cybersecurity issues. Through continuous learning and optimization, these algorithms can adapt to evolving attack scenarios and provide optimal control strategies to maintain system stability and mitigate the impact of cyberattacks. Furthermore, the development of these algorithms may lead to new learning algorithms and techniques that enhance the performance of AV systems. Therefore, integrating machine learning with AV system cybersecurity research opens a promising avenue for future work in this area.

[0262] What is presented Figure 9We demonstrate the successful implementation of an intelligent trigger threshold search mechanism that leverages machine learning techniques to iteratively explore the range of potential thresholds and determine the optimal threshold for the system. The threshold sequence in the figure depicts a search process that may require some iterative resources. Ultimately, however, this search results in a lower trigger rate and more efficient use of sampling resources. This intelligent mechanism can adapt to changing conditions and dynamically adjust the trigger threshold, significantly reducing the trigger rate and improving system efficiency. This mechanism achieves improved performance and robustness in real-world scenarios, opening up new possibilities for adaptive intelligent trigger thresholds in AV systems.

[0263] at last, Figure 10 A schematic diagram depicts the controller's trajectory under a DoS attack, which affects the control inputs and prevents the system from converging to zero. This result emphasizes the importance of the proposed controller in ensuring system reliability and safety, especially in industrial production environments. It also highlights the robustness and resilience of the proposed controller, making it a suitable choice for real-world applications requiring high safety standards. The findings of this study provide valuable insights for developing control strategies that can mitigate the impact of DoS attacks on cyber-physical systems and ensure their smooth operation under harsh conditions.

[0264] This embodiment explores the communication security issues of AV systems that rely on network control. First, a performance error estimation rule is established to estimate the performance degradation of AV systems under network attacks. Second, an improved data compression mechanism is developed to alleviate the communication network congestion problem caused by network attacks, thereby optimizing the allocation and use of network resources under limited bandwidth. Then, an adaptive learning I ETC strategy under mini-batch supervision is proposed to ensure the estimation of AV system performance error. In addition, the mathematical derivation is simplified by using more general LKFs. Finally, experimental results show that the proposed method effectively mitigates the impact of DoS attacks on AV communications while maintaining the accuracy of AV system performance error estimation. In addition, the proposed method is robust and reliable, and is suitable for practical applications with strict security requirements. This paper provides a theoretical basis for establishing a security defense mechanism for AV communications and demonstrates the effectiveness of the method proposed in this embodiment in improving the security and reliability of AV systems.

[0265] The above-described embodiments merely represent specific implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A safety controller design method for a networked control system, characterized in that: The method for analyzing performance error estimation of a networked control system under DoS attack and designing a safety controller under supervision of an adaptive learning algorithm comprises the following steps: Step 1: Establish TS fuzzy networked control system NCSs under DoS attack; Step 2: Formulate data compression rules under limited channel bandwidth; Step 3: Introduce IETC for adaptive learning under the supervision of mini-batch machine learning; Step 4: Develop a performance error evaluation mechanism to evaluate the control system performance error; In step 4, the control system performance error is evaluated based on the system performance evaluation and estimation rules of the reachable set concept, as follows: (1) Define the following ellipsoid boundaries : (2) The performance error estimation problem is transformed into the problem of finding an ellipsoid, as follows: (3) Given a real scalar If LKFsV is present t Satisfying V0=0,ω t Satisfies formula (17) and satisfies Then get Given a τ t ∈[a,b], any matrix and satisfy Then the following inequality is satisfied: Also includes: According to the new constraints to ensure the performance error estimation of the system, consider the TS fuzzy NCSs described in formula (10), where τ, γ, u min 、 and ρ are positive scalars; let Π(P) denote the boundary of the ellipsoid, assuming that there exist symmetric matrices P>0, Q>0, R, and matrices S, N1, N2 and satisfies the following LMI for all i,j=1,2,...,r: Λ(Ξ,Y,F)<0 (18) in: Λ(Ξ,Y,F)=Ξ+Y+F; Also includes: According to the new constraints to ensure the performance error estimation of the system, consider the TS fuzzy NCSs described in formula (10), where τ, γ, u min 、 and ρ are positive scalars; let Π(P) denote the boundary of the ellipsoid, assuming that there exist symmetric matrices P>0, Q>0, R, and matrices S, N1, N2, X, Y j and satisfies the following LMI for all i,j=1,2,...,r: in: yes i =[0 n×(i-1)n I n×n 0 n×(9-i) ],i=1,2,...,9.

2. The safety controller design method for a networked control system according to claim 1, characterized in that: The step 1 is specifically as follows: Consider TS fuzzy NCSs with the following fuzzy rules: Rule i: If λ 1t yes ,..., and λ mt yes So: Among them, x t is the state variable of the system, represents the external disturbance; the output of the system is z t , the control input signal is u t ; A i ,B i ,C i and E i is the parameter matrix; Fuzzy membership function δ i (μ t ) is defined as follows: in, Represents λ mt exist In addition, for all t≥0, the condition and Established; Standard fuzzy inference methods are used to transform NCSs into the following form: in: Assume that the sampling period of the system is represented by h, and the sampling time in the time interval kh is represented by t kh In order to describe DoS attacks, a preliminary formula is provided: in, Indicates the time period of the Nth DoS attack, where Indicates the number of attacks; in time When the attack signal is active, The value is 1, and at time t k+1h When the attack signal enters the dormant state, The value is 0; ) represents the period of time without DoS attack within the Nth time interval; then, the following conditions are established: The trigger threshold is represented by ρ, whose value ranges from 0 to 1; the variable Indicates the current status The status of the last successful transmission Differences between; variables Defined as in x tkh+mh Represents the last successful transmission status under DoS attack; the intensity of the attack is determined by Then, the transmission sequence is determined using the IETC condition. As shown below: Among them, the sampling time set of DoS attack is composed of represents, N represents the index of the attack; Indicates the active time period of the Nth DoS attack, where and t k+1h,N Respectively represent the start and end time of the attack; Using the fuzzy center balancer, the following input control is obtained: Rule j: If λ 1t yes ,..., and λ mt yes So: Then, the fuzzy controller is reformulated as follows: in, K j is the control gain matrix.

3. The method for designing a safety controller for a networked control system according to claim 2, wherein: The step 2 is specifically as follows: A flow compression function model is defined, denoted as T(·). The range of the flow compression function model is defined as follows: Define the model T(u t ) and formulate the following compression rules: (I) If the control input signal satisfies or set up (II) If the control input signal satisfies or set up (III) If the control input signal satisfies or Set T(u t )=0; (IV) If the control input signal satisfies and other situations, set The parameters and 0<θ<1, is T(u t )’s dead zone size; After the attack, the compressed control signal value is expressed as: Among them, the nonlinear function H(u t ) and vector U t Satisfying 1-γ≤H(u t )≤1+γ and Using Equation (2) and Equation (9), TS fuzzy NCSs can be expressed as follows:

4. The method for designing a safety controller for a networked control system according to claim 3, wherein: The step 3 is specifically as follows: Determine the optimal trigger threshold ρ within the specified interval θ and formulate a weakly convex optimization problem, considering the constraints of avoiding network congestion and maximizing bandwidth utilization in the presence of DoS attacks: Among them, the optimal trigger threshold ρ∈θ=[0,1]; the optimization target of determining ρ is represented by F, that is, Use the mini-batch proximal gradient method to find the optimal trigger threshold ρ within a given interval θ; generate a sequence ρ that converges to the optimal threshold by iteratively solving formula (11) k+1 ; The sequence is represented as follows: Let Q ρ : is a convex function with a Lipschitz continuous gradient, R ρ : is a possibly non-smooth convex function; the step size parameter is denoted by h l ; The iteration form is as follows: Combining the proximal operator with stochastic gradient descent, it is defined as follows: Among them, the random estimate of the gradient pass Get, which is defined as follows: Among them, the random estimate of the gradient is obtained by selecting from the set [n] = {1, 2, ..., n} the probability of q i >0 random index i selected k Calculated, and the convex function f ik Used to determine The average value of is used to calculate the gradient reference point.

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