Networked vehicle elastic control method capable of overcoming spoofing attacks and actuator faults

Abstract

The invention provides a networked vehicle elastic control method capable of overcoming spoofing attacks and actuator faults. The method comprises the following steps that a vehicle third-order nonlinear dynamic model reflecting the influence of unknown spoofing attacks, actuator faults and disturbance on networked vehicle queue control is established; setting a control target; an RBF neural network is adopted to process unknown nonlinear terms generated by spoofing attacks, actuator faults and disturbance; an improved fractional order command filter is introduced, and the problem of dimensionality explosion in the derivation process of a backstepping method is solved; introducing a Nussbaum function to eliminate the assumption that the unknown spoofing attack weight is positive; the validity of the algorithm is verified through numerical simulation. The invention designs an improved fractional order command filter based on a command filtering technology and a fractional order calculus theory. Compared with an integer order command filter, the filtering performance is obviously improved. Meanwhile, based on a finite time stability theory, the system can converge quickly.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle control, and in particular, to a resilient control method for a networked vehicle that can overcome deception attacks and actuator failures. Background Art

[0002] The development of intelligent transportation system (ITS) is one of the effective means to achieve safe, environmentally friendly and efficient traffic control. [1-2] Among them, the intelligent connected vehicle formation control uses cellular vehicle-to-everything (C-V2X) technology to share information such as position, speed, and acceleration between vehicles, thereby maintaining and tracking the distance between vehicles and vehicle speed. Compared with adaptive cruise control (ACC), it can obtain information more flexibly, has a faster response speed, and can maintain a smaller distance between vehicles. [3] , improving the stability of the queue and the traffic capacity. Since it forms feedback between the communication system and the physical system, it can be considered as a typical vehicular cyber physical system (VCPSs). [4] .

[0003] However, VCPSs are susceptible to communication delays, packet loss, and network attacks. In particular, security issues caused by network attacks have received much attention in recent years. [5] Typical network attacks are mainly divided into denial of service (DoS) attacks, replay attacks and spoofing attacks. Among them, the purpose of DoS attacks is to cut off the communication link and prevent vehicles from exchanging information. [6] The DoS attack on the vehicle is regarded as a communication packet loss problem. [7] A dynamic event triggering mechanism for sensing DoS attacks is proposed, and a distributed MPC controller with robustness constraints is designed. Replay attacks steal vehicle communication data and resend them after a certain delay to mislead the following vehicle. [8] Solve the control problem of linear system under DoS attack and replay attack. Both attacks can be treated as communication delay problem [9] ,Compared with this, deception attacks are more dangerous.,The attacker will tamper with the data packets sent by the communication,in order to manipulate the vehicle to achieve the attacker's expected behavior.,References [10-14]Advanced methods have been proposed to prevent and detect cyber attacks, but these cybersecurity methods only monitor cyber attacks and are not further integrated with vehicle control. In the field of connected fleet control, the method of reducing the impact of deception attacks is mostly to use Kalman filter theory

[15] , neural networks and observer theory to estimate and reconstruct the state information of the attacked vehicle.

[16] Based on improving the unbiased finite impulse response estimation and recovering the deception attack signal,

[17] A variable structure observer is designed to estimate the state under network attacks and delays. This type of method requires estimating the true state of all neighboring vehicles, which increases the complexity of calculation and has poor effect in practical engineering. Therefore, the elastic control of vehicle platoons remains a challenging problem.

[0004] Resilient control means that the system can adapt to changes in internal and external conditions, has a certain degree of flexibility and robustness, and can handle stable control problems under conditions such as vehicle platoons being attacked by network attacks.

[18] The designed controller can cope with the situation where the acceleration and speed of the vehicle are deceptively attacked, and improve the resilience of the vehicle platoon to deal with communication delays and network attacks.

[19] Fixed-time elastic control in the presence of deception attacks and external interference is studied, and an event trigger mechanism is introduced to save communication resources.

[20] A controller is designed for a system that is simultaneously attacked by DoS and spoofing, ensuring the asymptotic stability and platoon stability of vehicles under multiple network attacks.

[21] RBF neural network is used to compensate for deception attacks, however, it assumes that the attack weight is positive, which reduces the uncertainty of the attack and is very conservative in practical applications.

[0005] The above studies are all designed to be resilient control strategies against cyber attacks. In practical applications, actuators will gradually age due to their frequent actions, resulting in a series of failures such as stuck and reduced efficiency. Another important factor in the safety control of vehicle platoon systems is the problem of actuator failure. [22-24] A fault-tolerant controller is designed for actuator failure. However, in the field of connected vehicle platoon control, there is limited research on resilient control that simultaneously considers actuator failure compensation and network attacks. Since deception attacks tamper with state information, a large number of fault-tolerant control methods for actuator failures cannot be directly applied to systems after deception attacks. To solve this problem, the literature

[25] The effects of deception attacks and actuator failures are considered at the same time, and the Nussbaum function is used to solve the problem of unknown attack signal direction. The system is asymptotically stable when time tends to infinity.

[26] A finite-time adaptive estimator is designed to ensure timely compensation for deception attacks and handle actuator failures based on an observer, but it only considers the timeliness of the compensation signal and ignores the stability speed of the entire system. The problem of adaptive finite-time elastic control for nonlinear VCPSs systems considering both network attacks and actuator failures has not been fully studied.

[0006] References:

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[0038]

[32] JPYu, P.Shi, and L.Zhao, "Finite-time command filteredbacksteppingcontrol for a class of nonlinear systems," Automatica, vol.92, pp.173–180, 2018. Summary of the invention

[0039] Based on the technical problems mentioned in the above background technology, a resilient control method for a connected vehicle is provided that can overcome deception attacks and actuator failures.

[0040] The technical means adopted by the present invention are as follows:

[0041] A resilient control method for a connected vehicle that can overcome spoofing attacks and actuator failures includes the following steps:

[0042] Step 1: Establish a third-order nonlinear dynamic model of the vehicle that reflects the impact of unknown deception attacks, actuator failures, and disturbances on the platoon control of connected vehicles;

[0043] Step 2: Set control objectives;

[0044] Step 3: Use RBF neural network to handle unknown nonlinear terms generated by spoofing attacks, actuator failures, and disturbances;

[0045] Step 4: Introduce an improved fractional-order command filter to solve the problem of "dimensionality explosion" in the backstepping derivation process; introduce the Nussbaum function to eliminate the assumption that the unknown deception attack weight is positive;

[0046] Step 5: The effectiveness of the algorithm is verified through numerical simulation.

[0047] Furthermore, in step 1, the number of the pilot car is 0, and the number of the following car is i, i∈N, N={1,2,…,n}; x0(t), v0(t), a0(t) respectively represent the position, speed and acceleration of the pilot car; L represents the vehicle body length, d represents the reference signal of the distance between the i-th following car and the i-1-th following car, and each following car can receive the position, speed and acceleration transmitted by the leading car;

[0048] Then, the simplified third-order longitudinal nonlinear dynamic model of the following vehicle i is expressed as:

[0049]

[0050] Where τ represents the vehicle dynamics inertia delay; x i (t), v i (t), a i (t) represent the position, velocity and acceleration of the i-th following vehicle respectively; u i (t) represents the control input of the system; f i (t) represents the nonlinear part of the vehicle i dynamics model; according to the PF communication topology, a constant distance spacing strategy is adopted to establish the vehicle tracking error model:

[0051]

[0052]

[0053] Where D = L + d, L represents the vehicle body length, d is a constant representing the desired vehicle spacing;

[0054] Then the system state equation is expressed as:

[0055]

[0056]

[0057] Where Δf i (v i (t),a i (t),t)=f i-1 (t)-f i (t) represents an unknown nonlinear function;

[0058] Actuator failure may occur during the vehicle's response to the control signal. The actuator fails at time t∈t im,s ,t im,e The mathematical model of the failure in [)) is:

[0059]

[0060]

[0061] Among them, v i represents the actuator input, u i Indicates actuator output; 0≤l im <1, represents an unknown constant;

[0062] Considering the situation where the connected vehicles in the queue are attacked by unknown spoofing, the tracking error signal of the i-th following vehicle after being attacked is:

[0063]

[0064] in, represents the deception attack signal, i.e. λ(t) is an unknown time-varying signal; the unknown time-varying signal λ(t) is a bounded signal, that is, in, are all positive numbers; in addition, when 1+λ(t)=0, the state quantity of the system will be offset. Due to the limitation of controllability, the attack signal must satisfy 1+λ(t)≠0.

[0065] Furthermore, the actuator at time t∈t im,s ,t im,e [)) The failures encountered include:

[0066] 1) And l im=1, the output of the actuator is equal to the input, indicating that the actuator has no fault; that is, u i =υ i ;

[0067] 2) and 0 <l im When u<1, the output of the actuator is less than the input, indicating a partial failure of the actuator; that is, u i = l im υ i ;

[0068] 3) And l im = 0, the output of the actuator is independent of the input and is an unknown number Indicates that the actuator is stuck;

[0069] Furthermore, in step 2, the control objectives include: single vehicle stability and queue stability;

[0070] The single-vehicle stability is: each following vehicle can drive with a given spacing strategy, that is: x i-1 -x i →D; and the speed is consistent with the front car, that is: v i →v i-1

[0071] The queue stability satisfies that for μ1>0, ,satisfy:

[0072]

[0073] Furthermore, in step 3, the fractional derivative is defined as:

[0074]

[0075] Among them, α represents the order of the derivative, 0<α<1; the fractional order command filter is defined as:

[0076]

[0077] Among them, D α represents a fractional-order operator with 0<α<1; η j-1 represents the input of the filter, and All represent output; ρ1, ρ2, ρ3 all represent constants and satisfy 0<ρ1<1, ρ2>1, 0<ρ3<1;

[0078] The filtering error is defined as The filtering error compensation signal is designed as:

[0079]

[0080] in, a jl represents the design parameters, j = 1, 2, 3; l = 1, 2; to handle unknown deception attacks, then:

[0081]

[0082] Multiply both sides of the equation by β(t) = (1 + λ(t)) -1 ,have:

[0083]

[0084] Among them, β(t) satisfies |β(t)|≤β M And β M >0;

[0085] The introduced coordinate transformation is:

[0086]

[0087] in, represents the filter output; since the vehicle is under deception attack, the real error signal Unpredictable, so s j (j=1,2,3) is an unknown signal; the known signal will be used Rewrite the above formula as:

[0088]

[0089] Furthermore, in step 4, Nussbaum gain theory is used to process the deception attack signal of unknown direction and weight, and eliminate the assumption that λ(t)>0; for N(ξ)∈N, we have:

[0090]

[0091] Then N(ξ) is called Nussbaum function;

[0092] Let η j (j=1,2,3) is the virtual control law, is the adaptive law of the RBF neural network, N(ξ j ) is the Nussbaum function, ξ j (·) is 0, t s ) in the smooth function;

[0093] The virtual control law and adaptive law designed based on finite time stability theory and backstepping method are:

[0094]

[0095]

[0096] In addition, the control law and parameter update law are:

[0097]

[0098]

[0099] Compared with the prior art, the present invention has the following advantages:

[0100] The present invention is based on the third-order nonlinear dynamic model of the vehicle and designs a flexible control scheme according to the backstepping theory. It not only takes into account the situation where the vehicle communication is subjected to deception attacks, but also considers the actuator failure problem and ensures that the system error is ultimately uniformly bounded.

[0101] The present invention adopts an integral Lyapunov function combined with Nussbaum gain theory, and utilizes the characteristics of the Nussbaum function that the direction and size are constantly changing to eliminate the assumption that the attack weight is positive.

[0102] The present invention designs an improved fractional-order command filter based on command filtering technology and fractional-order calculus theory. Compared with integer-order command filters, the filtering performance is significantly improved. At the same time, based on the finite-time stability theory, the system can converge quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0104] Figure 1 Schematic diagram of the PF communication topology vehicle queue.

[0105] Figure 2 Schematic diagram of deception attack and actuator failure of the present invention.

[0106] Figure 3 It is a framework diagram of the finite time elastic control system of the present invention.

[0107] Figure 4 are the control signal and the actuator output signal of the present invention; wherein, (a) is the actuator failure time; and (b) is the control signal and the actuator output signal.

[0108] Figure 5Schematic diagram of the trajectory of a vehicle queue under the finite-time elastic controller of the present invention; wherein (a) is position; (b) is velocity; and (c) is acceleration.

[0109] Figure 6 Schematic diagram of adaptive parameters of the present invention.

[0110] Figure 7 Schematic diagram of the parameters of the Nussbaum function. (a) is the parameters of the Nussbaum function of the first following vehicle; (b) is the parameters of the Nussbaum function of the second following vehicle; (c) is the parameters of the Nussbaum function of the third following vehicle; (d) is the parameters of the Nussbaum function of the fourth following vehicle.

[0111] Figure 8 is the vehicle queue trajectory of the adaptive controller based on the reference document

[32] ; where (a) is the position; (b) is the velocity; and (c) is the acceleration.

[0112] Fig. 9 Schematic diagram of the comparison between deception attack and actuator failure time; where (a) is the deception attack time; (b) is the actuator failure time.

[0113] Fig.10 Schematic diagram of the comparison of experimental results of intelligent connected vehicle fleet based on finite-time elastic control; (a) is the distance; (b) is the speed. DETAILED DESCRIPTION

[0114] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0115] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0116] like Figure 1-10 As shown, the present invention provides a networked vehicle elastic control method that can overcome deception attacks and actuator failures, comprising the following steps:

[0117] Step 1: Establish a third-order nonlinear dynamic model of the vehicle that reflects the impact of unknown deception attacks, actuator failures, and disturbances on the platoon control of connected vehicles;

[0118] Step 2: Set control objectives;

[0119] Step 3: Use RBF neural network to handle unknown nonlinear terms generated by spoofing attacks, actuator failures, and disturbances;

[0120] Step 4: Introduce an improved fractional-order command filter to solve the problem of "dimensionality explosion" in the backstepping derivation process; introduce the Nussbaum function to eliminate the assumption that the unknown deception attack weight is positive;

[0121] Step 5: The effectiveness of the algorithm is verified through numerical simulation.

[0122] Furthermore, in step 1, the number of the pilot car is 0, and the number of the following car is i, i∈N, N={1,2,…,n}; x0(t), v0(t), a0(t) respectively represent the position, speed and acceleration of the pilot car; L represents the vehicle body length, d represents the reference signal of the distance between the i-th following car and the i-1-th following car, and each following car can receive the position, speed and acceleration transmitted by the leading car;

[0123] Then, the simplified third-order longitudinal nonlinear dynamic model of the following vehicle i is expressed as:

[0124]

[0125] Where τ represents the vehicle dynamics inertia delay; x i (t), v i (t), a i (t) represent the position, velocity and acceleration of the i-th following vehicle respectively; y i (t) represents the control input of the system; f i (t) represents the nonlinear part of the vehicle i dynamics model; according to the PF communication topology, a constant distance spacing strategy is adopted to establish the vehicle tracking error model:

[0126]

[0127] Where D = L + d, L represents the vehicle body length, d is a constant representing the desired vehicle spacing;

[0128] Then the system state equation is expressed as:

[0129]

[0130]

[0131] Where Δf i (v i (t),a i (t),t)=f i-1 (t)-f i (t) represents an unknown nonlinear function;

[0132] Actuator failure may occur during the vehicle's response to the control signal. The actuator fails at time t∈t im,s ,t im,e The mathematical model of the failure in [)) is:

[0133]

[0134]

[0135] Among them, v i represents the actuator input, u i Indicates actuator output; 0≤l im <1, represents an unknown constant;

[0136] Considering the situation where the connected vehicles in the queue are attacked by unknown spoofing, the tracking error signal of the i-th following vehicle after being attacked is:

[0137]

[0138] Where p = x, v, a, represents the deception attack signal, i.e. λ(t) is an unknown time-varying signal; the unknown time-varying signal λ(t) is a bounded signal, that is, in, are all positive numbers; in addition, when 1+λ(t)=0, the state quantity of the system will be offset. Due to the limitation of controllability, the attack signal must satisfy 1+λ(t)≠0.

[0139] Furthermore, the actuator at time t∈t im,s ,t im,e [)) The failures encountered include:

[0140] 1) And l im =1, the output of the actuator is equal to the input, indicating that the actuator has no fault; that is, u i =υ i ;

[0141] 2) and 0 <l im When u<1, the output of the actuator is less than the input, indicating a partial failure of the actuator; that is, u i = l im υ i ;

[0142] 3) And l im = 0, the output of the actuator is independent of the input and is an unknown number Indicates that the actuator is stuck;

[0143] Furthermore, in step 2, the control objectives include: single vehicle stability and queue stability;

[0144] The single-vehicle stability is: each following vehicle can drive with a given spacing strategy, that is: x i-1 -x i →D; and the speed is consistent with the front car, that is: v i →v i-1

[0145] The queue stability satisfies that for μ1>0, satisfy:

[0146]

[0147] Furthermore, in step 3, the fractional derivative is defined as:

[0148]

[0149] Among them, α represents the order of the derivative, 0<α<1; the fractional order command filter is defined as:

[0150]

[0151] Among them, D α represents a fractional-order operator with 0<α<1; η j-1 represents the input of the filter, and All represent output; ρ1, ρ2, ρ3 all represent constants and satisfy 0<ρ1<1, ρ2>1, 0<ρ3<1;

[0152] The filtering error is defined as The filtering error compensation signal is designed as:

[0153]

[0154] in, represents the design parameters, j = 1, 2, 3; l = 1, 2; to handle unknown deception attacks, then:

[0155]

[0156] Multiply both sides of the equation by β(t) = (1 + λ(t)) -1 ,have:

[0157]

[0158] Among them, β(t) satisfies |β(t)|≤β M And β M >0;

[0159] The introduced coordinate transformation is:

[0160]

[0161] in, represents the filter output; since the vehicle is under deception attack, the real error signal Unpredictable, so s j (j=1,2,3) is an unknown signal; the known signal will be used , rewrite the above formula as:

[0162]

[0163] Furthermore, in step 4, Nussbaum gain theory is used to process the deception attack signal of unknown direction and weight, and eliminate the assumption that λ(t)>0; for N(ξ)∈N, we have:

[0164]

[0165] Then N(ξ) is called Nussbaum function;

[0166] Let η j (j=1,2,3) is the virtual control law, is the adaptive law of the RBF neural network, N(ξ j ) is the Nussbaum function, ξ j (·) is 0, t s ) in the smooth function;

[0167] The virtual control law and adaptive law designed based on finite time stability theory and backstepping method are:

[0168]

[0169]

[0170] In addition, the control law and parameter update law are:

[0171]

[0172]

[0173] Embodiment 1:

[0174] The effectiveness of the designed control system is verified by numerical simulation. Based on a vehicle platoon consisting of a leader vehicle and four following vehicles, the initial position [x0,x0,x2,x3,x4] = [100,90,80,70,60] m, the expected spacing d = 7.5 m, and the nonlinear part of the vehicle dynamics model is The vehicle dynamics parameters are τ = 0.25, θ = 1.2, A i =2.2, C di =0.35, m i =1650,d mi =0.2sin(t), L=2.5. The acceleration of the leader car is as follows:

[0175]

[0176] The controller and filter design parameters are as follows:

[0177] Table 1: Controller design parameters

[0178]

[0179] Table 2: Fractional-order command filter design parameters

[0180]

[0181] Table 3: Filter error compensation signal design parameters

[0182]

[0183] Figure 4 (a) and (b) show the time when the actuator failure occurs, that is, the actuator failure u=0.7υ+1 occurs at time t∈[15,18]∪[26,32]∪[48,51]. In addition, the simulated deception attack signal is The number of nodes in the hidden layer of the RBF neural network is selected as 5, and the other parameters are selected as follows: jk =0.2, c 1k =[-2-1 0 1 2], c 2k =[c 1k c 1k c 1k ]T , c 3k =[c 1k c 1k c 1k c 1k ] T , the neural network inputs are: Figure 5 (a), (b), and (c) are the simulation results of vehicle platoon control. It can be seen that the vehicle tracking performance is good and it can handle actuator failures and network attacks at the same time. The controller of the present invention is based on the finite time stability theory, so the vehicle platoon can quickly reach stability in a very short time.

[0184] Figure 6 and Figure 7 are the trajectories of adaptive parameters and Nussbaum parameters respectively. Figure 6 The adaptive parameters in can solve the problem of unknown attacks, failures and interferences on the system, making the system more resilient. Figure 7 It can be seen from the figure that the Nussbaum function changes direction at t = 0.8s. Figure 5 It can be seen that this transformation adapts to the correct control direction, enabling the system to handle attack signals from unknown directions.

[0185] The control method designed in reference

[32] was compared with the control method designed in reference

[32] . Reference

[32] designed an adaptive neural network control method under actuator failure. Using the same model parameters, the experimental results based on reference

[32] are shown in Figure 8 (a), (b), (c). After the spoofing attack, a large shock occurs, which shows that this method cannot ensure the stability of the system when it is attacked by spoofing.

[0186] Embodiment 2:

[0187] Based on a 1:10 scale miniature intelligent networked vehicle, the effectiveness of the algorithm is verified on the networked vehicle experimental platform. The chassis structure of the miniature vehicle uses the six-core RK3399 chip as the main computing platform, the STM32F103RCT6 chip with the ARM Cortex-M3 core architecture as the main control platform, and uses the GY-53 infrared ranging module to measure the actual vehicle distance, the incremental Hall encoder module to measure the actual speed, and the MPU-9250 nine-axis sensor module to measure the vehicle acceleration. The AP6354 vehicle-mounted WIFI chip and the local area network are used to achieve vehicle-to-vehicle communication.

[0188] The central control system interface of the experimental platform can issue start, stop, speed change and other instructions to the leader car through the cloud central control system. The following cars all adopt a distributed control method and send information such as the distance between vehicles and speed collected by the sensors to the cloud SQL database for storage.

[0189] In the experiment, the actual vehicle distance measured is subtracted from the expected distance to obtain the distance error, and the speed and acceleration of the front vehicle are obtained by wireless communication to obtain the speed error. In addition, considering the unknown nonlinear terms and disturbances in the vehicle dynamics model, the derivative of the vehicle acceleration is calculated according to the calculation formula given in equation (1), and the acceleration is obtained by integrating it. Finally, the acceleration error is obtained by subtracting it from the acceleration measured by the front vehicle sensor. After the connected fleet is started, the central control end sends instructions to simulate actuator failures and network attacks. The time of sending instructions is shown in Fig. 9 (a), (b). The deception attack signal is The simulated actuator fault signal is u=0.7υ+1.

[0190] After receiving the command, the following vehicle calculates the actuator output and tracking error respectively. The vehicle control law u is calculated in the RK3399 chip i (t), integrate to obtain the expected speed of the vehicle, and send it to the STM32 chip through serial communication to control the pin output PWM drive motor to adjust the vehicle speed. Set the expected spacing to D = 40cm, and the initial spacing between vehicles is 0.52m and 0.45m respectively. The leader car travels at a speed of 0.4m / s in 0-18s, decelerates to 0.2m / s in 18-57s, and accelerates to 0.4m / s in 57-80s. Under deception attacks and actuator failure conditions, the vehicle spacing and speed can quickly track the expected values. Therefore, the controller design method proposed in the present invention is effective.

[0191] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0192] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0193] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of the units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0194] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0195] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0196] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes.

[0197] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A resilient control method for connected vehicles that can overcome spoofing attacks and actuator failures, characterized in that: The following steps are involved: Step 1: Establish a third-order nonlinear dynamic model of the vehicle that reflects the impact of unknown deception attacks, actuator failures, and disturbances on the platoon control of connected vehicles; Step 2: Set control objectives; Step 3: Use RBF neural network to handle unknown nonlinear terms generated by spoofing attacks, actuator failures, and disturbances; Step 4: Introduce an improved fractional-order command filter to solve the problem of "dimensionality explosion" in the backstepping derivation process; introduce the Nussbaum function to eliminate the assumption that the unknown deception attack weight is positive; Step 5: The effectiveness of the algorithm is verified through numerical simulation.

2. The method for resilient control of connected vehicles capable of overcoming spoofing attacks and actuator failures according to claim 1, characterized in that: In step 1, the number of the pilot car is 0, and the number of the following car is i, i∈N, N={1,2,…,n}; x0(t), v0(t), a0(t) respectively represent the position, speed and acceleration of the pilot car; L represents the vehicle length, d represents the reference signal of the distance between the i-th following car and the i-1-th following car, and each following car can receive the position, speed and acceleration transmitted by the leading car; Then, the simplified third-order longitudinal nonlinear dynamic model of the following vehicle i is expressed as: Where τ represents the vehicle dynamics inertia delay; x i (t), v i (t), a i (t) represent the position, velocity and acceleration of the i-th following vehicle respectively; u i (t) represents the control input of the system; f i (t) represents the nonlinear part of the vehicle i dynamics model; according to the PF communication topology, a constant distance spacing strategy is adopted to establish the vehicle tracking error model: Where D = L + d, L represents the vehicle body length, d is a constant representing the desired vehicle spacing; Then the system state equation is expressed as: Where Δf i (v i (t),a i (t),t)=f i-1 (t)-f i (t) represents an unknown nonlinear function; Actuator failure may occur during the vehicle's response to the control signal. The actuator fails at time t∈t im,s ,t im,e The mathematical model of the failure in [)) is: Among them, i represents the actuator input, u i Indicates actuator output; 0≤l im <1, represents an unknown constant; Considering the situation where the connected vehicles in the queue are attacked by unknown deception, the tracking error signal of the i-th following vehicle after being attacked is: Where p = x, v, a, represents the deception attack signal, i.e. is an unknown time-varying signal; the unknown time-varying signal λ(t) is a bounded signal, that is, in, are all positive numbers; in addition, when 1+λ(t)=0, the state quantity of the system will be offset. Due to the limitation of controllability, the attack signal must satisfy 1+λ(t)≠0.

3. The method for resilient control of connected vehicles capable of overcoming spoofing attacks and actuator failures according to claim 2, characterized in that: The actuator is at time t∈t im,s ,t im,e [)) The failures encountered include: 1) And l im =1, the output of the actuator is equal to the input, indicating that the actuator has no fault; that is, u i =v i ; 2) and 0 <l im When u<1, the output of the actuator is less than the input, indicating a partial failure of the actuator; that is, u i = l im v i ; 3) And l im = 0, the output of the actuator is independent of the input and is an unknown number Indicates that the actuator is stuck; 4. The method for resilient control of connected vehicles capable of overcoming spoofing attacks and actuator failures according to claim 1, characterized in that: In step 2, the control objectives include: single vehicle stability and queue stability; The single-vehicle stability is: each following vehicle can drive with a given spacing strategy, that is: x i-1 -x i →D; and the speed is consistent with the front car, that is: v i →v i-1 The queue stability satisfies that for μ1>0, satisfy:

5. The method for resilient control of connected vehicles capable of overcoming spoofing attacks and actuator failures according to claim 1, characterized in that: In step 3, the fractional derivative is defined as: Among them, α represents the order of the derivative, 0<α<1; the fractional order command filter is defined as: Among them, D α represents a fractional-order operator with 0<α<1; η j-1 represents the input of the filter, and All represent output; ρ1, ρ2, ρ3 all represent constants and satisfy 0<ρ1<1, ρ2>1, 0<ρ3<1; The filtering error is defined as The filter error compensation signal is designed as: in, a jl represents the design parameters, j = 1, 2, 3; l = 1, 2; to handle unknown deception attacks, then: Multiply both sides of the equation by β(t) = (1 + λ(t)) -1 ,have: Among them, β(t) satisfies |β(t)|≤β M And β M >0; The introduced coordinate transformation is: in, represents the filter output; since the vehicle is under deception attack, the real error signal Unpredictable, so s j (j=1,2,3) is an unknown signal; the known signal will be used Rewrite the above formula as:

6. The resilient control method for connected vehicles capable of overcoming spoofing attacks and actuator failures according to claim 1, characterized in that: In step 4, Nussbaum gain theory is used to process the deception attack signal of unknown direction and weight, and eliminate the assumption that λ(t)>0; for N(ξ)∈N, there is: Then N(ξ) is called Nussbaum function; Let η j (j=1,2,3) is the virtual control law, is the adaptive law of the RBF neural network, N(ξ j ) is the Nussbaum function, ξ j (·) is 0, t s ) in the smooth function; The virtual control law and adaptive law designed based on finite time stability theory and backstepping method are: In addition, the control law and parameter update law are:

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