Intelligent control algorithm design method for unmanned ground vehicle

Abstract

The present invention discloses a method for designing an intelligent control algorithm for an unmanned ground vehicle, comprising: constructing a networked control system NCSs and an event triggering mechanism based on integration; performing traffic compression under limited channel bandwidth; optimizing the triggering threshold based on machine learning; and estimating the performance error of the networked control system NCSs. The present invention proposes a new method for solving the security and reliability challenges of NCSs when facing DoS attacks.

Description

Technical Field

[0001] The invention relates to the technical field of networked control systems, and in particular to an intelligent control algorithm design method for an unmanned ground vehicle. Background Art

[0002] The rapid development of digital computing in the mid-20th century led to the emergence of digital data control (DDC) systems, which applied computers to control engineering and promoted the development of DDC systems in industrial production. DDC systems use digital signals and microprocessors to control the target system. However, due to some limitations of DDC systems, they are difficult to be widely popularized [1]. This led to the introduction of distributed control system (DCS) technology, which uses centralized distributed digital technology to control each process. Despite its advantages, DCS systems have some limitations in compatibility and integration [2]. In the 1970s, fieldbus control systems (FCSs) were the first products used in industrial control applications in digital communications. These systems used analog signals to communicate with devices such as sensors and actuators, but had limited capabilities in handling complex control applications [3]. Networked control systems (NCSs) were proposed in the early 21st century, enhancing system reliability and enabling advanced detection, management, and optimization of underlying data scheduling. As a result, NCSs began to become a popular research topic.

[0003] In the existing work, the authors summarized the work and basic problems about NCSs. They used different underlying network scheduling protocols to solve the delay problem in NCSs and analyzed the stability of NCSs. In [6], a novel method was proposed to solve the stability problem of NCSs, and a controller was designed for the mean square stability of NCSs. In [7], the authors studied NCSs with nonlinear characteristics and proposed some criteria to ensure the stability of nonlinear NCSs based on linear NCSs. In [8], the authors focused on the security issues of NCSs and proposed a new event-triggered strategy design for 2-DoF helicopter systems to deal with denial of service (DoS) attacks. In

[10] , the authors proposed an innovative method to improve the cyber-physical security of energy-saving power systems in hybrid electric vehicles to resist complex cyber attacks.

[0004] With the rapid development of the information technology industry, NCSs have reached a higher level. Currently, the CSMA / CD (collision detection) protocol of the IEEE802.3 standard is used in NCSs to achieve high-speed communication network transmission, in which each node competes for resources equally without any priority difference

[11] . However, competition between communications may cause network congestion because the channel can only serve one request at a time, resulting in a large number of requests queuing and causing network transmission delays. The QoS mechanism of communication defines and enforces rules to prioritize network traffic by evaluating different factors such as the bandwidth required for each request, delay sensitivity, packet loss tolerance, etc., thereby alleviating network congestion problems

[12] . At a certain moment in the entire communication channel, an abnormal increase in user demand for network resources may cause security issues. The TCP / IP protocol of the data link layer has inherent vulnerabilities when establishing a three-way handshake link within a computer network. Hackers can exploit these vulnerabilities to launch malicious attacks on the target system

[13] . Hackers may use multiple computers to access the target host at the same time, creating demand that exceeds the inherent capacity of the network, causing network congestion, performance degradation, and ultimately downtime. This type of attack is called a DoS attack

[14] .

[0005] In

[15] , the security control problem of NCSs under DoS attacks was proposed as a key research issue. In addition, in

[16] , the authors proposed an event-triggered control method to analyze two situations with and without DoS attacks. In

[17] , Cheng et al. found that DoS attacks are periodic, so they studied the relationship between DoS periodicity and decay rate. In order to better analyze the performance of NCSs, Peng et al. proposed a novel random event-triggered communication scheme in

[18] to analyze the H∞ performance of NCSs under DoS attacks. Preventing DoS attacks is an important research topic for many scholars. One practical approach is to segment the network, reducing its size and making it more manageable. This can help prevent the attack from spreading and causing widespread damage. Another useful strategy is to deploy an intrusion detection and prevention system that can identify and block malicious traffic. However, fundamentally, DoS attacks are designed to create network congestion, ultimately disrupting the normal operation of the server. One way to effectively defend against such attacks is to find a way to handle more network requests under limited bandwidth without causing congestion

[19] .

[0006] Hacker attacks may have a negative impact on the performance of computer systems. In order to ensure stability under DoS attacks, many researchers have proposed effective control strategies. However, it is usually necessary to analyze whether the error in system performance can be estimated and whether it is within an acceptable range.

[0007] [1]H.M.Newman,Directdigitalcontrolofbuilding systems:Theoryandpractice,NewYork:Wiley,1994.

[0008] [2]F.L.Lian,J.Moyne and D.Tilbury,Network design consideration fordistributed control systems,IEEE Transactions onControl SystemsTechnology,vol.10,no.2,pp.297-307,2002.

[0009] [3]G.Schickhuber and O.McCarthy,Distributed fieldbus and controlnetwork systems,Computing\&Control EngineeringJournal,vol.8,no.1,pp.21-32,1997.

[0010] [4]W.Zhang,M.S.Branicky and S.M.Phillips,Stability ofnetworkedcontrol systems,IEEE Control Systems Magazine,vol.21,no.1,pp.84-99,2001.

[0011] [5]G.C.Walsh,H.Ye andL.G.Bushnell,Stability analysisofnetworkedcontrol systems,IEEE Transactions on Control Systems Technology,vol.10,no.3,pp.438-446,2002.

[0012] [6]H.J.Gao,X.Y.Meng and T.W.Chen,Stabilization of networked controlsystems with a new delay characterization,IEEE Transactions onAutomaticControl,vol.53,no.9,pp.2142-2148,2008.

[0013] [7]B.P.Jiang,H.R.Karimi,Y.G.Kao and C.C.Gao},Takagi-Sugeno model-based event-triggered fuzzy sliding-mode control ofnetworked control systemswith semi-Markova switching,IEEE Transactions on Fuzzy Systems,vol.28,no.4,pp.673-683,2020.

[0014] [8]X.B.Gao,F.Q.Deng,P.Y.Zeng and H.Y.Zhang,Adaptive neural event-triggered control ofnetworked Markovjump systems underhybrid cyberattacks,IEEE Transactions onNeuralNetworks andLearning Systems,DOI:10.1109 / TNNLS.2021.3105532.

[0015] [9]X.Cai,K.B.Shi,K.She,P.G.Park,S.M.Zhong and O.M.Kwon,Event-triggered control strategy for2-DoF helicopter system under DoS attacks,IEEETransactions on Transportation Electrification,DOI:10.1109 / TTE.2022.3227086.

[0016]

[10] L.L.Guo,J.Ye and L.Du,Cyber-physical security ofenergy-efficientpowertrain systemin hybrid electric vehicles against sophisticatedcyberattacks,IEEE Transactions on TransportationElectrification,vol.7,no.2,pp.636-648,2020.

[0017]

[11] R.A.GuptaandM.Y.Chow,Networkedcontrol system:overviewandresearchtrends,IEEETransactions on IndustrialElectronics,vol.57,no.7,pp.2527-2535,2010.

[0018]

[12] M.Karakus and A.Durresi,Quality of service(QoS)in softwaredefined networking(SDN):A survey,JournalofNetworkandComputerApplications,vol.80,no.15,pp.200-218,2017.

[0019]

[13] G.Carl,G.Kesidis,R.R.Brooks and S.Rai,Denial-of-service attack-detection techniques,IEEE Internet Computing,vol.10,no.1,pp.82-89,2006.

[0020]

[14] A.HovavandJ.D.Arcy,The impactofdenial-of-serviceattackannouncements onthemarketvalue offirms,RiskManagementandInsuranceReview,vol.6,no.2,pp.97-121,2003.

[0021]

[15] S.Amin,A.Cardenas,and S.Sastry,Safe and secure networked controlsystems under denial-of-service attacks,HybridSystems:Computation andControl,vol.5469,pp.31-45,2009.

[0022]

[16] C. Peng and H. T. Sun, Switching-like event-triggered control for networked control systems under malicious denial of service attacks, IEEE Transactions on Automatic Control, vol. 65, no. 9, pp. 3943-3949, 2020.

[0023]

[17] Z. H. Cheng, D. Yue, S. G. Shen, S. L. Hu and L. Chen, Resilient event-triggered controller synthesis of networked control systems under periodic DoS jamming attacks, IEEE Transactions on Cybernetics, vol. 49, no. 12, pp. 4271-4281, 2019.

[0024]

[18] C. Peng, J. C. Wu and E. G. Tian, Stochastic event-triggered H∞ control for networked systems under denial of service attacks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 7, pp. 4200-4210, 2022.

[0025]

[19] M. H. Bhuyan, H. J. Kashyap, D. K. Bhattacharyya and J. K. Kalita, Cyberattack detection for electric vehicles using physics-guided machine learning, IEEE Transactions on Transportation Electrification, vol. 7, no. 3, pp. 2010-2022, 2021. Summary of the Invention

[0026] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide an intelligent control algorithm design method for an unmanned ground vehicle. The present invention proposes a new method to solve the security and reliability challenges of NCSs when facing DoS attacks.

[0027] To achieve the above object, the technical solution adopted by the present invention is: a method for designing an intelligent control algorithm for an unmanned ground vehicle, comprising the following steps:

[0028] Step 1: Construct networked control systems (NCSs) and event triggering mechanisms based on integration;

[0029] Step 2: compress traffic under limited channel bandwidth;

[0030] Step 3: Optimize the trigger threshold based on machine learning;

[0031] Step 4: Estimate the performance error of the networked control system NCSs.

[0032] As a further improvement of the present invention, the step 1 is specifically as follows:

[0033] Consider a networked control system NCSs with dual communication channels and external disturbances as follows:

[0034]

[0035] in x t : = x(t) is the state vector; ω t :=ω(t) external input interference; u t : =u(t) control input signal; A, B and C are given system constant matrices;

[0036] Assume that the sampling time of the k-time interval is t k , design π(t k )as follows:

[0037]

[0038] in, is the time interval of communication interruption; Indicates the time interval for normal communication; is the number of cycles; T * Indicates the time period of communication interruption, T>0 is the DoS attack interval;

[0039] The constraint design of dual-channel IETM is as follows:

[0040]

[0041] Among them, σ∈[0,1] is the trigger threshold; s represents the attack intensity, π(t k ) is the hacker attack time; the delay between every two successful sampling times in the sensor-to-controller channel d ca is the time delay of the controller-to-actuator channel; x t is the current state system thread, Indicates the system status of the last successful transmission; set DoS attack to cause error information and Where Φ>0 is a constant matrix;

[0042] Next successful transmission time in case of random data loss It can be defined as:

[0043]

[0044] Among them, Θ(t k ) is the random trigger signal loss, Θ(t k ) is Prob{Θ(t k )=0}=θ,Prob{Θ(t k )=1}=1-θ and θ∈[0,1] is the random probability triggering signal loss.

[0045] As a further improvement of the present invention, the control input signal in the networked control system NCSs is designed as follows:

[0046]

[0047] where K is the control gain matrix to be solved.

[0048] As a further improvement of the present invention, the step 2 is specifically as follows:

[0049] The flow compression function model T(·) is defined as follows:

[0050]

[0051] in, represents the i-th sub-compression function T i (·) initial compression value; The value of depends on the data compression density; choose the compression function T i (x i ), (i=1,2,3,...,n) as follows:

[0052]

[0053] Among them, β i =(1-δ i ) / (1+δ i ); the flow compression value is limited to the fan-shaped bounded area between the slope proportional function (1-β) and (1+β),

[0054] Transform the bounded sector region into and

[0055] Defining Error Therefore, the measured value of the compressed control signal after being attacked in formula (6) is expressed as:

[0056]

[0057] in ΔT is the sum of the compression errors;

[0058] Finally, the compressed control input signal of formula (9) is substituted into formula (1); NCSs is rewritten as follows:

[0059]

[0060] As a further improvement of the present invention, the step 3 is specifically as follows:

[0061] The threshold selection problem is transformed into a weak convex optimization problem with the following constraints:

[0062]

[0063] where the regularization function R(·) is specified as the usual χ2 regularization function, and represents the error information generated by DoS attack; G is the trigger condition defined in formula (4);

[0064]

[0065] in, is the Lagrangian function, is the Lagrange function multiplier;

[0066] The non-smooth part in formula (12) is separated and represented by r. The separation process is expressed as follows:

[0067]

[0068] The augmented Lagrangian is expressed as follows:

[0069]

[0070] Where η is the Lagrange multiplier, ε is a scalar, is a bounded variable and sets Get no The augmented Lagrangian is as follows:

[0071]

[0072] Solve for σ using the following iterative steps max :

[0073]

[0074] Further rewrite the update process of r in formula (16); after omitting the terms irrelevant to r, use the proximal operator to solve σ max The problem is transformed as follows:

[0075]

[0076] The alternating direction method of multipliers ADMM in machine learning is used to optimize the selection of the trigger threshold σ.

[0077] As a further improvement of the present invention, the step 4 is specifically as follows:

[0078] (1) Define the concept of performance error estimation; Limit The ellipsoid:

[0079]

[0080] (2) Convert the performance error estimation problem into an ellipsoid problem:

[0081]

[0082] Where P>0 is a real constant matrix;

[0083] (3) Given a real scalar If there exists LKFs V0=0, then ω t Satisfies formula (18), and Established, we can get V t ≤1,

[0084] Attack time series The average DoS attack interval is equal to T a If there exists S0 ≥ 0 and T a , we can get the DoS attack interval as follows:

[0085]

[0086] in and It is the attack sequence Over a period of time (t,T);

[0087] Given τ t ∈[a,b], any matrix and satisfy The following inequality is satisfied:

[0088]

[0089] in:

[0090]

[0091] As a further improvement of the present invention, it also includes:

[0092] For NCSs with DoS attack in formula (10), there exists a positive scalar d sc ,d ca , σ max , s, θ and symmetric matrix P>0, M1, M2, H i (i=1,2,3),Q,R, and any matrices N1, N2 of appropriate dimensions such that the following LMIs hold:

[0093]

[0094] Y(Λ,Ω)≤0 (21) in:

[0095]

[0096] in:

[0097]

[0098] The LKFs are selected as follows:

[0099]

[0100] in:

[0101]

[0102] The time derivative of is given by:

[0103]

[0104] It is expressed as the following formula:

[0105]

[0106] In V 2t An asymmetric LKF is constructed in part of which For trimming V 2t , With V 4t Combined processing; first, V 3t is cut as follows:

[0107]

[0108] Using the result of Jensen's inequality, It can be scaled as follows:

[0109]

[0110] According to the result of formula (26), V 2t The pruning process is as follows:

[0111]

[0112] Then, V t p and V t q The time derivative of is derived as follows:

[0113]

[0114] The integral term in equation (29) is scaled using the integral inequality:

[0115]

[0116] Then V t q Written as follows:

[0117]

[0118] Considering the triggering conditions of formula (4) under the machine learning algorithm and the result of Jensen's inequality, the following inequality is obtained:

[0119]

[0120] In addition, for the system of formula (10), there exist arbitrary matrices N1 and N2 that satisfy the following equation:

[0121]

[0122] Finally, according to the designed performance error estimation rule, the following inequality is obtained:

[0123]

[0124] When formula (33) holds true, it means It satisfies the error estimation rule, which shows that x T Px≤V t ≤1; therefore, the set of performance error estimates is included in Π(P).

[0125] As a further improvement of the present invention, it also includes:

[0126] For NCSs with DoS attack in formula (10), there exists a positive scalar d sc ,d ca , σ max , s, θ, μ and symmetric matrix and any matrices Y, X of appropriate dimensions such that the following LMIs hold:

[0127]

[0128]

[0129] in:

[0130]

[0131] in:

[0132]

[0133] The beneficial effects of the present invention are:

[0134] The present invention proposes a new performance error estimation rule based on reachable sets; by evaluating the performance error estimate of the system, an appropriate ellipse boundary can be determined to ensure that the performance error is estimable; it should be noted that a more accurate ellipse boundary provides a better performance error estimate; therefore, estimating the performance error of NCSs under attack is crucial for analyzing and studying system performance under harsh conditions; the proposed performance error estimation rule provides a valuable tool for determining whether the error is within a controllable range, which can guide the development of more effective control strategies to ensure the safety of the system. Based on the above analysis, the present invention proposes an integral-based event triggering mechanism based on a machine learning algorithm to ensure that the performance error of NCSs under DoS attacks can be estimated. The main contributions of the present invention are as follows:

[0135] (1) NCSs under dual-channel DoS attacks are proposed to analyze the time delay phenomenon in network communications.

[0136] (2) Hacker attacks may cause network congestion and communication delays. A traffic compression model is established to alleviate the network congestion caused by DoS attacks.

[0137] (3) An integration-based event triggering mechanism based on a machine learning algorithm is established to intelligently select the optimal threshold σ to reduce resource usage.

[0138] (4) In the CarSim-Simulink joint platform experiment, the system error was evaluated while minimizing resource usage. BRIEF DESCRIPTION OF THE DRAWINGS

[0139] Figure 1 is a schematic diagram of network load and information throughput in Example 1 of the present invention;

[0140] Figure 2 It is a flow compression curve diagram of the T(·) function in Example 1 of the present invention;

[0141] Figure 3 This is a schematic diagram of flow signal compression error in Example 1 of the present invention;

[0142] Figure 4 This is a schematic diagram of the structure of a networked control system under a DoS attack in Example 1 of the present invention;

[0143] Figure 5 A schematic diagram of an autonomous ground vehicle model for path tracking in Embodiment 2 of the present invention;

[0144] Figure 6 This is a dynamic response diagram of the AGV under DoS attack in Example 2 of the present invention;

[0145] Figure 7 A schematic diagram of an error evaluation Π(P) ellipsoid boundary in Embodiment 2 of the present invention;

[0146] Figure 8 This is another schematic diagram of the boundary of the error evaluation Π(P) ellipsoid in Embodiment 2 of the present invention;

[0147] Fig. 9 This is a schematic diagram of system response under data compression in Embodiment 2 of the present invention;

[0148] Fig.10 This is another schematic diagram of system response under data compression in Embodiment 2 of the present invention;

[0149] Fig.11 is a system response diagram when the trigger signal is lost in Example 2 of the present invention;

[0150] Fig.12 is a system response diagram under different attack intensities in Example 2 of the present invention;

[0151] Fig.13 is another system response diagram under different attack intensities in Example 2 of the present invention;

[0152] Fig.14 This is a system response diagram under the third different attack intensities in Example 2 of the present invention. DETAILED DESCRIPTION

[0153] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0154] Example 1

[0155] A method for designing an intelligent control algorithm for an unmanned ground vehicle, comprising:

[0156] 1. Networked control system and event trigger mechanism based on integration:

[0157] In this embodiment, NCSs with dual communication channels and external interference are considered as follows:

[0158]

[0159] in x t : = x(t) is the state vector; ω t :=ω(t) external input interference; u t : =u(t) controls the input signal; A, B and C are the given system constant matrices.

[0160] Hardware modularization and advances in microelectronics have made systems smaller and more reliable than previous systems. Such systems can be expanded as needed by adding control nodes, shadow nodes, and actuator nodes to produce NCSs. However, the use of the Internet for information exchange in network control systems also brings security issues. Unfortunately, it is well known that the TCP / IP protocol has vulnerabilities that can be exploited by hackers and may cause the server to crash. This embodiment uses a periodic DoS attack with adjustable attack intensity to solve this problem. Specifically, assume that the sampling time of the k time interval is t k , this embodiment designs π(t k )as follows:

[0161]

[0162] in, is the time interval of communication interruption; Indicates the time interval for normal communication; is the number of cycles; T * Indicates the time period of communication interruption, T>0 is the DoS attack interval.

[0163] The core of DoS attack is to use a large amount of access information to access a host at the same time. Multiple users may try to occupy the same channel, but a channel only allows one user to use it at a time. Therefore, multiple access attempts cause users to be in a waiting state, resulting in a decrease in the overall throughput of the communication network.

[0164] The communication within NCSs is established through the three-way handshake protocol based on the TCP / IP protocol at the network layer. However, due to the existence of vulnerabilities in the protocol, DoS attacks may exploit them and cause network congestion. Figure 1 It is shown that the load of the channel self-regulates as the throughput increases, and the throughput begins to self-regulate once it reaches an inflection point, at which point the channel throughput becomes saturated. A DoS attack launched by a hacker can cause the throughput of a channel to drop rapidly because the channel is flooded with requests. In response, network routers and switches make adjustments to ensure that the throughput of the channel remains within normal range. However, repeated DoS attacks can cause the network to collapse, resulting in the inability to transmit signals.

[0165] Then, the constraint design of dual-channel IETM is as follows:

[0166]

[0167] Among them, σ∈[0,1] is the trigger threshold; s represents the attack intensity, π(t k ) is the hacker attack time; the delay between every two successful sampling times in the sensor-to-controller channel d ca is the time delay of the controller-to-actuator channel; x t is the current state system thread, Indicates the system status of the last successful transmission; set DoS attack to cause error information and Where Φ>0 is a constant matrix.

[0168] Then, the signal transmission of this channel may cause signal loss, and the next successful transmission time under random data loss is It can be defined as:

[0169]

[0170] Among them, Θ(t k ) is the random trigger signal loss, Θ(t k ) is Prob{Θ(t k )=0}=θ,Prob{Θ(t k )=1}=1-θ and θ∈[0,1] is the random probability triggering signal loss.

[0171] Please note that the control input signals in NCSs are designed as follows:

[0172]

[0173] where K is the control gain matrix to be analyzed, e t Defined in (4).

[0174] 2. Traffic compression method under limited channel bandwidth:

[0175] DoS attacks may cause server downtime, but delivering more data traffic within limited bandwidth helps reduce congestion, improve throughput, and keep communication channels running smoothly. To achieve this, this embodiment proposes a new traffic compression function model called T(·), which compresses data in a way that takes up less space while maintaining its quality. This reduces the amount of traffic that needs to be transmitted, improves throughput, and minimizes the risk of congestion and delays. The traffic compression function model is an important tool for defending against DoS attacks and can make communication networks run more efficiently. The model is defined as follows:

[0176]

[0177] in, represents the i-th sub-compression function T i (·) initial compression value; The value of depends on the data compression density. In this embodiment, the compression function T is selected i (x i )(i=1,2,3,...,n) as follows:

[0178]

[0179] Among them, β i =(1-δ i ) / (1+δ i ).from Figure 2 and Figure 3 It can be seen that the flow compression value is limited to the fan-shaped bounded area between the slope proportional function (1-β) and (1+β).

[0180] Similarly, the bounded sector region can be transformed into and Defining Error Therefore, the measured value of the compressed control signal in (6) after being attacked can be expressed as

[0181]

[0182] in ΔT is the sum of the compression errors.

[0183] Finally, the compressed control input signal (9) is substituted into (1). NCSs can be rewritten as follows:

[0184]

[0185] Higher throughput and less network congestion are required to ensure system stability and high-quality signal transmission efficiency. This embodiment develops a flow compression function model (such as Figure 2 The model compresses the data stream while maintaining acceptable errors, so that more requests can be processed within a limited bandwidth. Although this approach may introduce some external errors and interference, it ensures the normal operation of the system, while alleviating network congestion caused by DoS attacks and preventing system paralysis.

[0186] 3. Threshold optimization solution based on machine learning:

[0187] Finding the optimal trigger threshold σ in the interval [0,1] is another research problem of this embodiment. This embodiment transforms the threshold selection problem into a weak convex optimization problem with the following constraints:

[0188]

[0189] where the regularization function R(·) is specified as the usual χ2 regularization function, and represents the error information generated by the DoS attack; G is the trigger condition defined in (4).

[0190]

[0191] in is the Lagrangian function, is the Lagrange function multiplier.

[0192] The regularization function R(·) may not be smooth, but the variable segmentation method can be used to segment the non-smooth part. To solve this problem, this embodiment separates the non-smooth part in (12) and represents it with r. Then, the separation process is expressed as follows:

[0193]

[0194] The augmented Lagrangian can be expressed as follows:

[0195]

[0196] Where η is the Lagrange multiplier and ε is a scalar. is a bounded variable and sets Get no The augmented Lagrangian is as follows:

[0197]

[0198] For simplicity, the The update process on σ can be solved using the following iterative steps: max :

[0199]

[0200] We can further rewrite the updating process of r in (16). After omitting the terms irrelevant to r, we can solve σ using the proximal operator. max The problem is transformed as follows:

[0201]

[0202] Selecting an appropriate trigger threshold σ will affect the convergence speed and smoothness of NCSs. In addition, σ can also affect the average residence time and trigger rate of the trigger mechanism, which plays an important role in solving communication resource constraints. Therefore, this embodiment uses the alternating direction method of multipliers (ADMM) in machine learning to optimize the selection of σ and effectively solve large-scale linear matrix inequality problems.

[0203] 4. Performance error estimation scheme of NCSs:

[0204] DoS attacks can cause increased channel load and communication congestion, which can significantly affect system performance. Finding a method to estimate the performance degradation of a system after an attack is of great significance to solving this problem and has become a new research direction in this field. Based on the concept of reachable sets, a set of system performance error estimation rules is proposed. By understanding reachable sets and how these rules are applied to a system, its performance can be better predicted and measures can be taken to mitigate the impact of DoS attacks.

[0205] (1) Define the concept of performance error estimation. The ellipsoid:

[0206]

[0207] (2) Convert the performance error estimation problem into an ellipsoid problem:

[0208]

[0209] Where P>0 is a real constant matrix.

[0210] (3) Given a real scalar If there exists LKFs V0=0, then ω t satisfies (18), and Established, we can get V t ≤1,

[0211] In network control systems, hacker attacks may seriously affect the performance of the system, leading to instability, reduced reliability, and damage to network infrastructure. These attacks may cause high latency, network outages, and other types of damage. Therefore, it is important to evaluate the performance degradation of the system after being attacked by hackers and to analyze and study the performance of the system under attack. This embodiment formulates rules for evaluating system performance errors, which can guide the research on issues such as system reliability, stability, and robustness under attack.

[0212] Attack time series The average DoS attack interval is equal to T a If there exists S0 ≥ 0 and T a , we can get the DoS attack interval as follows:

[0213]

[0214] in and It is the attack sequence Over a period of time (t,T).

[0215] Given τ t ∈[a,b], any matrix and satisfy The following inequality is satisfied:

[0216]

[0217] in:

[0218]

[0219] 5. Main results:

[0220] This section demonstrates the estimation of the performance error of the DoS attack system (10). This embodiment also introduces a signal compression mechanism and an IETM based on machine learning to alleviate network congestion and save bandwidth resources. The constraints of the controller gain matrix K are established in Theorem 1, and the solution of the controller gain matrix is ​​given in Theorem 2.

[0221] Theorem 1 For NCSs (10) with DoS attack, there exists a positive scalar d sc ,d ca , σ max , s, θ and symmetric matrix P>0, M1, M2, H i (i=1,2,3),Q,R, and any matrices N1, N2 of appropriate dimensions such that the following LMIs hold:

[0222]

[0223] Y(Λ,Ω)≤0 (21)

[0224] in:

[0225]

[0226] and Y(Λ,Ω) and Shown in the Appendix.

[0227] Proof: The LKFs are chosen as follows:

[0228]

[0229] in:

[0230]

[0231] x t 、x s Symbols such as , M, etc. are defined in the appendix.

[0232] V t , The time derivative of is given by:

[0233]

[0234] here, It is expressed as the following formula:

[0235]

[0236] In V 2t An asymmetric LKF is constructed in part of which For trimming V 2t , With V 4t Combined for joint processing. First, V 3t is cut as follows:

[0237]

[0238] Using the result of Jensen's inequality, It can be scaled as follows:

[0239]

[0240] According to the result of (26), V 2tThe pruning process is as follows:

[0241]

[0242] Then, V t p and V t q The time derivative of is derived as follows:

[0243]

[0244] Here, the integral term in (29) is scaled using the integral inequality in Lemma 1. We have:

[0245]

[0246] Then V t q It can be written as follows:

[0247]

[0248] Considering the triggering condition (4) under the machine learning algorithm and the result of Jensen's inequality, the following inequality is obtained:

[0249]

[0250] Furthermore, for system (10), there exist arbitrary matrices N1 and N2 that satisfy the following equations:

[0251]

[0252] Finally, according to the designed performance error estimation rule, the following inequality is obtained:

[0253]

[0254] When (33) holds, it means It satisfies the error estimation rule, which shows that x T Px≤V t ≤ 1. Therefore, the set of performance error estimates is included in Π(P).

[0255] In existing methods, constructing LKF usually requires a symmetric method. However, this embodiment proposes a method called V 2t The asymmetric construction method reduces the constraints on decision variables, thereby reducing the conservatism of the criterion. In addition, V 3t It is divided into two parts, To compensate V 2t The asymmetric terms in the LKF are ensured to meet the requirements.

[0256] V 4t and Consider constructing V together t q In addition, the integral inequality is used to deal with V t q The integral term in , and introduce This approach not only simplifies the derivation process, but also reduces the conservatism of the criterion to a certain extent.

[0257] Theorem 2 For NCSs (10) with DoS attack, there exists a positive scalar d sc ,d ca , σ max , s, θ, μ and symmetric matrix and any matrices Y, X of appropriate dimensions such that the following LMIs hold:

[0258]

[0259] in:

[0260]

[0261] and Shown in the Appendix.

[0262] The design controller gain matrix and other symbols are defined as follows:

[0263] K=YX -1 , N1=X -1 ,N2=μX -1

[0264]

[0265] Combine (20) and (21) with X T Premultiplied with X, we obtain LMIs (34) and (35).

[0266] Algorithm 1 shows the σ determined by the machine learning algorithm. k The optimization value of ∈[0,1] is used to update the trigger threshold and LMIs solution. The solution is iteratively refined using the Yalmip toolbox in Python and Matlab until the optimal σ is obtained. k .

[0267]

[0268] appendix:

[0269] x s:=x(s),x θ :=x(θ),

[0270] x s+ν :=x(s+ν),e t :=e(t)

[0271]

[0272] M=[M1,M2],

[0273] φ=col{e4,e1-e2,d ca e1-e5},

[0274] e i =[0 n×(i-1)n I n×n 0 n×(9-i) ],i=1,2,...,9

[0275]

[0276]

[0277] Example 2

[0278] This example uses the AGV dynamics model to evaluate the effectiveness of the proposed method (see Figure 5 ).

[0279] The parameter matrix is ​​defined as follows:

[0280]

[0281] Where, m = 1500kg, I z =2500kg·m 2 , l s =0.8m, I f =1.3m,l r =1.4m, C f =C r =40000N / rad, C = [1,1,-1,1]. Other definitions in the experimental part are omitted for simplicity.

[0282] The experiment is divided into two steps to verify the results. First, the Yalmip toolbox is used to solve the given constraints to determine the optimal error parameters. Specifically, the trigger threshold is set to σ k=0.7568, the compression ratio is 0.3, and the communication delays of channel 1 and channel 2 are d sc = 0.2 and d ca = 0.5. In addition, the trigger data loss rate θ = 0.4 is considered. In the second step, the Yalmip toolbox is used to solve the constraints and obtain the optimal performance error estimation parameters The experimental results are shown in Table 1, which show that the proposed method effectively alleviates the impact of communication delay and loss rate on system performance, providing conclusive evidence.

[0283] Table 1: Maximum performance evaluation parameters under different attack strengths s as follows:

[0284]

[0285]

[0286] According to the data in Table 1, as the attack intensity increases, the error evaluation parameters of the system continue to decrease. For example, when the attack intensity is s = 1, the computer takes 1.63 seconds to determine However, when the attack intensity is doubled to s = 2, the solution obtained by Theorem 1 is This indicates that the evaluation parameter has decreased by 37.39%. In addition, we select μ = 1 and controller gain matrix K = 10 -4 ×[10.88,-29.28,-67.47,-0.016], the trajectory of the AGV was verified using the CarSim-Simulink platform. Figure 6 As shown in Figure 2, despite the DoS attack from hackers, the system exhibits a stable trajectory and eventually converges to about 0. It is worth noting that the systematic performance error is the basis for estimating the next stage.

[0287] Table 2: The maximum communication delay d under different data compression ratios is as follows:

[0288]

[0289] In the case of limited network bandwidth, communication delays during signal transmission may be inevitable. However, it should be noted that even under these constraints, the system can still exhibit excellent reliability and anti-interference to handle large communication delays. In this regard, this embodiment proposes a new strategy to enhance data transmission efficiency and reduce system time delay by increasing the data compression ratio. The results show that the maximum acceptable delay for different compression ratios can be illustrated in Table 2. For example, when the compression ratio is set to 0.3, the dual-channel communication delay is 0.7429. As the compression ratio increases, the signal transmission efficiency of the system is significantly improved, which in turn leads to a reduction in overall time delay. This observation emphasizes the importance of data compression in improving the effectiveness of the system in the face of communication delays and DoS attacks.

[0290] Based on the controller gain matrix obtained previously, the appropriate ellipsoid boundary can be determined to limit the impact of DoS attacks on the system error. The state trajectory of the system is shown in Figure 6 As shown, we can see that they all converge to about 0. To estimate the performance loss caused by the hacker attack, Figure 7 and Figure 8 The ellipse bounds of Π(P) are shown, which provides a visualization of the ellipse bounds and illustrates how it can be used to limit the impact of a DoS attack on system performance. The ellipse bounds are a useful tool for estimating the performance degradation of a system after a DoS attack.

[0291] like Figure 7 and Figure 8 By comparing the semi-major axes of the ellipses in these figures, it can be observed that the accuracy of the error trajectory changes with the performance error estimation parameters. The most accurate error estimation of the ellipse boundary is achieved when . In addition, the length of the semi-major axis of the ellipse corresponds to the accuracy of the error estimation. In line with the theoretical results, the larger value leads to a more precise estimate.

[0292] One of the main challenges to be solved in this embodiment is the congestion problem caused by DoS attacks on the communication system. The proposed method involves using data compression to alleviate the network congestion problem. In order to evaluate the effectiveness of this method, Fig. 9 and Fig.10 The dynamic response of the system under different traffic compression ratios is demonstrated. The results show that high-quality traffic compression can ensure smooth convergence of the system under DoS attacks. However, it should be noted that a higher compression ratio does not necessarily guarantee better performance, as compression may introduce errors in the system. Specifically, a higher compression ratio may lead to more errors and increase the uncertainty of the results. Therefore, it is necessary to find an optimal compression ratio that balances the trade-off between traffic reduction and error reduction in the system.

[0293] Various factors can undermine the reliability of network communications, including the sensitivity of data transmission to packet loss. Packet loss rates can significantly affect system stability and convergence. Fig.11 As shown, different packet loss rates affect the convergence of the system in different ways. A high packet loss rate can produce unstable oscillations, which can lead to instability in practical engineering applications. In addition, the loss of trigger signals due to packet loss may have a negative impact on the convergence of the system. The method proposed in this embodiment provides a solution to the problem of trigger data loss, ensuring that the system is more stable and efficient. The method of this embodiment is intended to enhance the system's ability to resist interference with communication delays and packet loss, ensuring that the system can operate reliably even under difficult conditions.

[0294] When subjected to high-intensity DoS attacks, the system exhibits more oscillations, leading to instability and destroying its convergence. Fig.12 As shown in Figure 2, the system trajectories under different attack intensities lead to shocks that become stronger as the attack intensity increases. Choosing an appropriate trigger threshold σ k It is crucial to mitigate these effects and ensure the convergence of the system. This problem is formulated as a weakly convex optimization problem, and the ADMM algorithm in machine learning is used to search for σ in the interval [0,1]. k The method proposed in this embodiment provides a practical and effective solution for selecting a trigger threshold, which is crucial for maintaining the stability and reliability of the system when facing DoS attacks.

[0295] Table 3 shows the k The trigger time and trigger rate of the system under the value The results show that when σ 1 =0.1276, the trigger rate is as high as 0.9073. However, after continuous learning and improvement, a better σ k Specifically, when σ k+1 =0.7328, the trigger rate is reduced to 0.5602. The machine learning algorithm iteratively searches for the appropriate σ k The value significantly improves resource efficiency. Each search reduces the trigger rate to a certain extent, and finally selects the optimal σ max value.

[0296] Table 3: The number of triggers and the trigger rate under the machine learning algorithm are as follows:

[0297] Machine Learning Process Trigger times Trigger rate <![CDATA[Update iteration σ 1 = 0.1276]]> 1351 90.73％ <![CDATA[Update iteration σ 2 = 0.3781]]> 1241 81.53％ <![CDATA[Update iteration σ k-1 = 0.4064]]> 901 75.71％ <![CDATA[Update iteration σ k = 0.6983]]> 614 67.32％ <![CDATA[Update iteration σ k+1 = 0.7328]]> 521 56.02％

[0298] Fig.13 and Fig.14The successful transmission and dwell time of the trigger signal are shown. The intelligent trigger threshold search mechanism uses machine learning to iteratively traverse the range [0,1] to find the optimal threshold, denoted as σ, such as the sequence σ 1 →…→σ 2 →…→σ k-1 →…→σ k →…as shown. Although iteration resources are consumed in the process, this embodiment can reduce the trigger rate to save sampling resources. This optimization is crucial in actual industrial production. This is one of the important contributions of this embodiment, because the mechanism proposed in this embodiment can significantly reduce the sampling frequency and improve the overall efficiency of the system. This is crucial for reliable and cost-effective industrial production. The proposed mechanism can adapt to changing conditions and effectively reduce the trigger rate by dynamically adjusting the trigger threshold using machine learning.

[0299] This embodiment proposes a comprehensive solution to address the challenge of performance error estimability in dual-channel NCSs under DoS attacks. The proposed solution includes the analysis of network congestion caused by QoS management mechanism and the development of a signal compression mechanism to alleviate the congestion caused by DoS attacks. In addition, an asymmetric LKF has been constructed and divided into two parts to compensate for the asymmetric LKF and increase the LKF energy, thereby reducing the conservatism of the standard. In addition, an IETM based on machine learning algorithm has been developed to estimate the performance error of NCSs. The proposed solution has been verified on the CarSim-Simulink joint platform, and the results show the feasibility and effectiveness of the proposed method. In general, this embodiment proposes a new method to solve the security and reliability challenges of NCSs in the face of DoS attacks.

[0300] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for designing an intelligent control algorithm for an unmanned ground vehicle, characterized in that: Based on performance error estimation and machine learning supervision of dual-channel NCSs under DoS attack, the method comprises the following steps: Step 1: Construct networked control systems (NCSs) and event triggering mechanisms based on integration; Step 2: compress traffic under limited channel bandwidth; Step 3: Optimize the trigger threshold based on machine learning; Step 4, estimating the performance error of the networked control system NCSs; The step 1 is specifically as follows: Consider a networked control system NCSs with dual communication channels and external disturbances as follows: in x t : = x(t) is the state vector; ω t :=ω(t) external input interference; u t : =u(t) control input signal; A, B and C are given system constant matrices; Assume that the sampling time of the k-time interval is t k , design π(t k )as follows: in, is the time interval of communication interruption; Indicates the time interval for normal communication; is the number of cycles; T * Indicates the time period of communication interruption, T>0 is the DoS attack interval; The constraint design of dual-channel IETM is as follows: Among them, σ∈[0,1] is the trigger threshold; s represents the attack intensity, π(t k ) is the hacker attack time; the delay between every two successful sampling times in the sensor-to-controller channel d ca is the time delay of the controller-to-actuator channel; x t is the current state system thread, Indicates the system status of the last successful transmission; set DoS attack to cause error information and Where Φ>0 is a constant matrix; Next successful transmission time in case of random data loss It can be defined as: Among them, Θ(t k ) is the random trigger signal loss, Θ(t k ) is Prob{Θ(t k )=0}=θ,Prob{Θ(t k )=1}=1-θ and θ∈[0,1] is the random probability trigger signal loss; The control input signal design in the networked control system NCSs is as follows: where K is the control gain matrix to be solved; The step 2 is specifically as follows: The flow compression function model T(·) is defined as follows: in, represents the i-th sub-compression function T i (·) initial compression value; The value of depends on the data compression density; choose the compression function T i (x i ), (i=1,2,3,...,n) as follows: Among them, β i =(1-δ i ) / (1+δ i ); the flow compression value is limited to the fan-shaped bounded area between the slope proportional function (1-β) and (1+β), Transform the bounded sector region into and Defining Error Therefore, the measured value of the compressed control signal after being attacked in formula (6) is expressed as: in ΔT is the sum of the compression errors; Finally, the compressed control input signal of formula (9) is substituted into formula (1); NCSs is rewritten as follows:

2. The intelligent control algorithm design method for an unmanned ground vehicle according to claim 1, characterized in that: The step 3 is as follows: The threshold selection problem is transformed into a weak convex optimization problem with the following constraints: where the regularization function R(·) is specified as the usual χ2 regularization function, and represents the error information generated by DoS attack; G is the trigger condition defined in formula (4); in, is the Lagrangian function, is the Lagrange function multiplier; The non-smooth part in formula (12) is separated and represented by r. The separation process is expressed as follows: The augmented Lagrangian is expressed as follows: Where η is the Lagrange multiplier, ε is a scalar, is a bounded variable and sets Get no The augmented Lagrangian is as follows: Solve for σ using the following iterative steps max : Further rewrite the update process of r in formula (16); after omitting the terms irrelevant to r, use the proximal operator to solve σ max The problem is transformed as follows: The alternating direction method of multipliers ADMM in machine learning is used to optimize the selection of the trigger threshold σ.

3. The intelligent control algorithm design method for an unmanned ground vehicle according to claim 2, characterized in that: The step 4 is specifically as follows: (1) Define the concept of performance error estimation; Limit The ellipsoid: (2) Convert the performance error estimation problem into an ellipsoid problem: Where P>0 is a real constant matrix; (3) Given a real scalar If there exists LKFs V0=0, then ω t Satisfies formula (18), and Established, we can get V t ≤1, Attack time series The average DoS attack interval is equal to T a If there exists S0 ≥ 0 and T a , we can get the DoS attack interval as follows: in and It is the attack sequence Over a period of time (t,T); Given τ t ∈[a,b], any matrix and satisfy The following inequality is satisfied: in:

4. The intelligent control algorithm design method for an unmanned ground vehicle according to claim 3 is characterized in that: Also includes: For NCSs with DoS attack in formula (10), there exists a positive scalar d sc ,d ca , σ max , s, θ and symmetric matrix P>0, M1, M2, H i (i=1,2,3),Q,R, and any matrices N1, N2 of appropriate dimensions such that the following LMIs hold: Y(Λ,Ω)≤0 (21) in: in: The LKFs are selected as follows: in: The time derivative of is given by: It is expressed as the following formula: In V 2t An asymmetric LKF is constructed in part of which For trimming V 2t , With V 4t Combined processing; first, V 3t is cut as follows: Using the result of Jensen's inequality, It can be scaled as follows: According to the result of formula (26), V 2t The pruning process is as follows: Then, V t p and V t q The time derivative of is derived as follows: The integral term in equation (29) is scaled using the integral inequality: Then V t q Written as follows: Considering the triggering conditions of formula (4) under the machine learning algorithm and the result of Jensen's inequality, the following inequality is obtained: In addition, for the system of formula (10), there exist arbitrary matrices N1 and N2 that satisfy the following equation: Finally, according to the designed performance error estimation rule, the following inequality is obtained: When formula (33) holds true, it means It satisfies the error estimation rule, which shows that x T Px≤V t ≤1; therefore, the set of performance error estimates is included in Π(P).

5. The intelligent control algorithm design method for an unmanned ground vehicle according to claim 4, characterized in that: Also includes: For NCSs with DoS attack in formula (10), there exists a positive scalar d sc ,d ca , σ max , s, θ, μ and symmetric matrix and any matrices Y, X of appropriate dimensions such that the following LMIs hold: in: in:

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