Fixed-time optimal control method for intelligent connected vehicles against DoS attacks based on hierarchical structure

Abstract

This application provides a fixed-time optimal control method for intelligent connected vehicles to resist DoS attacks based on a hierarchical structure. The method includes: step 1, constructing an intelligent connected vehicle system model; the intelligent connected vehicle system model includes a leading vehicle and a following vehicle; step 2, designing a hierarchical optimal control method based on the intelligent connected vehicle dynamics model; step 3, based on event-triggered optimal control, using an online algorithm based on reinforcement learning to determine the weight vector approximate optimal control law. This application provides a hierarchical cooperative optimal control method. The virtual reference layer determines a distributed elastic reference signal to ensure that the leading intelligent agent and the reference signal are consistent at a fixed time in the event of intermittent communication interruption caused by DoS attacks. The tracking control layer designs an optimal control strategy based on the reference signal and event triggering mechanism to achieve tracking of the reference signal within a fixed time and optimize the overall system performance.

Description

Technical Field

[0001] The present application relates to the technical field of intelligent connected vehicles, and in particular to a fixed-time optimal control method for intelligent connected vehicles to resist DoS attacks based on a hierarchical structure. Background Art

[0002] Road transportation is the lifeblood of the national economy, but existing road infrastructure is difficult to expand. Traffic congestion and exhaust pollution caused by insufficient road capacity and a rapidly increasing number of vehicles pose significant challenges to traffic management. With the rapid development of autonomous driving and V2V (vehicle-to-vehicle) communication technologies, the sharing of vehicle status information (position, speed, acceleration) has improved the stability of vehicle platoons and reduced response delays. Research has shown that platooning can effectively improve road efficiency, fuel economy, and driving safety. The goal of platooning control is to ensure that vehicles in a platoon maintain equal spacing and travel at a constant speed, without collisions between adjacent vehicles.

[0003] However, the open nature of information transmission and high-speed vehicle mobility make connected autonomous vehicle platoon control systems vulnerable to malicious cyberattacks, such as data theft, tampering, and interruption, posing a significant threat to user privacy, property, and safety. Denial of service (DoS) attacks are a potential type of attack on connected vehicles. These attacks typically interfere with the radio frequency of the vehicle-to-vehicle network or block V2V network access with a large number of requests, thereby preventing information exchange between vehicles and disrupting inter-vehicle data transmission and platoon control systems.

[0004] The collaborative control of intelligent connected vehicles typically employs distributed control, meaning the control protocol relies solely on information exchange between connected vehicles and their neighbors. While this approach can achieve platoon control and effectively utilize computing and communication resources, it cannot guarantee optimal overall performance and cost. Limited system resources necessitate the development of a control approach that balances control objectives with performance and cost.

[0005] Traditional optimal control design methods use coupled cooperative errors to establish performance indicator functions and the Hamilton-Jacobi-Bellman equation. This significantly increases the complexity of obtaining the optimal value function and control strategy, and fails to balance control objectives and performance indicators under DoS attacks. Summary of the Invention

[0006] This application provides a fixed-time optimal control method for intelligent connected vehicles to resist DoS attacks based on a hierarchical structure, which can be used to solve the technical problems that the optimal value function and optimal control strategy are too complex and cannot balance the control objectives and performance indicators under DoS attacks.

[0007] This application provides a fixed-time optimal control method for intelligent connected vehicles to resist DoS attacks based on a hierarchical structure, the method comprising:

[0008] Step 1: Build an intelligent connected vehicle system model; the intelligent connected vehicle system model includes a leading vehicle and a following vehicle;

[0009] Step 2: Design a hierarchical optimal control method based on the mathematical model of the intelligent connected vehicle powertrain;

[0010] The layers include a virtual reference signal generation layer and a tracking control layer. The virtual reference signal generation layer integrates attack resilience algorithms and distributed algorithms to resist the impact of DoS attacks. The tracking control layer introduces an event trigger mechanism into the optimal control strategy to balance the relationship between communication computing resources and system performance optimization.

[0011] Step 3: Based on event-triggered optimal control, an online algorithm based on reinforcement learning is used to determine the weight vector to approximate the optimal control law.

[0012] Furthermore, step 1 is to construct a smart connected vehicle system model, including:

[0013] The longitudinal dynamics equation of the i-th, i=1,2,...,N intelligent connected vehicles is described as:

[0014]

[0015] where p i represents the position of vehicle i, represents the speed of vehicle i, represents the acceleration of vehicle i, F i e represents the vehicle driving force, and the dynamic equation is expressed as:

[0016]

[0017] Where u i represents the throttle input of vehicle i, represents the component of gravity of vehicle i parallel to the road surface,

[0018] represents air resistance. Assuming that all vehicles are moving in the same direction, sig(v i +v w )=1, m represents the vehicle weight, represents the body resistance of vehicle i, g represents the acceleration due to gravity, represents the angle between the plane of the i-th vehicle and the road slope, m a Indicates the air density, S a represents the cross-sectional area of the vehicle, d crepresents the air resistance coefficient, v w represents the wind speed, and T represents the inertia time of the power transmission system.

[0019] Let x i =[p i ,v i ,a i ] T is the state vector of the following connected vehicle, x0 is the nonlinear function of the leading connected vehicle, and f(x0) is the nonlinear function of the leading connected vehicle. is a nonlinear function following the connected car, is the external disturbance of the following connected vehicle, ω0 represents the external disturbance of the leader connected vehicle, and the system models of the leading vehicle and the following vehicle i are expressed as:

[0020]

[0021] and

[0022]

[0023] in and is the coefficient matrix, y i and y0 represent the output states of the leading vehicle and the following vehicle respectively, is the output matrix.

[0024] Furthermore, in step 2, based on the mathematical model of the power of the intelligent connected vehicle, a hierarchical optimal control method is designed, including:

[0025] Step 21, constructing a virtual reference signal generation layer;

[0026] Step 22: Construct a tracking control layer. The tracking control layer is used to formulate an optimal control plan to ensure that the reference signal is tracked within a fixed time and to achieve optimal system comprehensive performance indicators.

[0027] Furthermore, step 21, constructing a virtual reference signal generation layer, includes:

[0028] The DoS attack signal is defined as:

[0029]

[0030] Where k represents the number of attacks, t ak represents the time when the attack signal is activated, τ k Indicates the attack residence time, t a(k+1) Indicates the end time of the kth attack, A k =[t ak ,t k ),t k =t ak +τk Indicates the attack range;

[0031] The virtual reference signal is designed as follows:

[0032]

[0033] where K1 and K2 are gain matrices of moderate dimensions, is the indicator function, ρ1 is a positive constant satisfying is a positive constant, V1 is the Lyapunov function designed to determine the stability of the implementation; a ij The adjacency matrix A=(a ij )∈R N×N The element of a ij >0 means that the following connected vehicle i can obtain status information from the following connected vehicle j, otherwise a ij =0;N i represents the set of connected vehicles that have communication connections with the i-th connected vehicle; d i Indicates the communication connection between the i-th follower connected car and the leader connected car. When the leader and the i-th follower connected car are connected, d i >0, otherwise d i =0; represents the elements of the adjacency matrix under the attack signal, represents the communication connection between the leader and the i-th following connected vehicle under the attack signal.

[0034] Based on the reference signal, the time it takes for the reference signal to be consistent with the fixed time of the leading connected vehicle is calculated as:

[0035]

[0036] Where γ is the state convergence rate, ρ1 is a positive constant satisfying is a positive constant, T 21 yes The minimum positive solution, T 22 yes The minimum positive solution of A constant limiting the total duration of a DoS attack.

[0037] Furthermore, in step 22, a tracking control layer is constructed. The tracking control layer is used to formulate an optimal control scheme to ensure that the reference signal is tracked within a fixed time and the overall system performance index is optimized, including:

[0038] Step 221, constructing a tracking error model;

[0039] Based on the designed virtual reference signal and the following connected vehicle dynamics model, the tracking error state is defined as e i =Cxi -Cξ i , the error model is:

[0040]

[0041] in

[0042]

[0043] Step 222: Construct a performance index function related to the error state and the control law:

[0044] Based on the set tracking error state e i , define the performance index function as:

[0045]

[0046] In the formula Meet L i (0,0)=0,P i >0 and Q i >0 is a symmetric positive definite matrix, allowing control u i ∈U(Ω) piecewise continuous, satisfying u i (0) = 0 and at the rest time T max The internal error system of the connected vehicle is stabilized.

[0047] Step 223, define the Hamiltonian function and propose the general form of the optimal control law:

[0048] Define the Hamiltonian function:

[0049]

[0050] in Represents the optimal value function V i (e i )About e i Find the partial derivative and transpose; the optimal value function is solved by Obtained, expressed as:

[0051]

[0052] Optimal control law for:

[0053]

[0054] Among them B T Represents the transpose of the coefficient matrix B of the connected vehicle system. C T represents the transpose of the output matrix C of the connected vehicle system. Step 224, proposes an event triggering rule and an event triggering optimal control law for achieving optimal control within a fixed time:

[0055] set up is the triggering time sequence of the i-th error state, s represents the s-th triggering time, is the observation error, Indicates the trigger time The tracking error value at in is the sth trigger interval of the ith error state. Under the event trigger mechanism, the event trigger optimal control law is expressed as:

[0056]

[0057] The triggering time sequence is determined by the following event triggering rules:

[0058]

[0059] Among them, 0<ω1<1 is a positive constant, λ max (Q i ) represents the matrix Q i The maximum eigenvalue of min (P i ) represents the matrix P i The minimum eigenvalue of min (Q i ) represents the matrix Q i The minimum eigenvalue, L ui yes The Lipschitz constant satisfied.

[0060] Furthermore, step 3, based on event-triggered optimal control, uses an online algorithm based on reinforcement learning to determine the weight vector to approximate the optimal control law; including:

[0061] Step 31, constructing an approximate value function of a judgment neural network;

[0062] Step 32, estimating the value function and proposing the corresponding optimal control law;

[0063] Step 33, define the weight error vector, Bellman function and error E i ;

[0064] Step 34: Determine the weight vector update rule and pause time.

[0065] Furthermore, step 31 is to construct an approximate value function of a judgment neural network, including:

[0066] The approximate value function and gradient of the judging neural network are expressed as:

[0067]

[0068] In the formula represents the weight vector, represents the activation function, is the number of neurons, ∈ i is the approximation error, and the upper bound is ∈ im .

[0069] Furthermore, step 32, estimating the value function and proposing the corresponding optimal control law, includes:

[0070] Since the weight vector W i Unknown, let the estimate be The value function is expressed as:

[0071]

[0072] in It is V i (e i ), and then the optimal control strategy can be obtained, which is expressed as:

[0073]

[0074] Based on the estimated value function and the event-triggered optimal control law, the estimate of the Hamiltonian function is expressed as:

[0075]

[0076] Further, in step 33, the weight error vector, Bellman function and error E are defined. i ;include:

[0077] Define the weight vector error separately Bellman error and function E i for

[0078] in express In t l The residual function at time η il represents η i In t l The value at time t l For time series The elements satisfy 0≤t l ,...,t s <t,s>0.

[0079] Furthermore, step 34, determining the weight vector update rule and pause time, includes:

[0080] In order to accurately estimate the weight vector Learning law is α The update rule is

[0081]

[0082] Based on the fixed-time stability theory, the dwell time for the tracking error model to stabilize is:

[0083]

[0084] in is a constant, is a constant, r1 is a constant, is a positive constant, is a constant, Representation matrix

[0085] Y i =[η i1 ,η i2 ,...,η ir ], is a constant, and τ1 is a positive constant.

[0086] In order to resist the impact of DoS attacks on system performance, this application designs a hierarchical cooperative optimal control method. The virtual reference layer designs a distributed elastic reference signal to ensure that the leader agent and the reference signal are consistent at a fixed time in the event of intermittent communication interruptions caused by DoS attacks. The tracking control layer designs an optimal control strategy based on the reference signal and event triggering mechanism to achieve fixed-time tracking of the reference signal and optimize the overall system performance.

[0087] Since it is difficult to obtain an accurate expression for the value function related to the event-triggered optimal control strategy, this application designs and evaluates a self-learning optimization control framework based on the reinforcement learning algorithm. The goal is to minimize the Bellman error within a fixed time, and the weights are updated along the gradient descent direction of the performance indicator function to ensure the search efficiency and path optimization, thereby approximating the optimal control strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 A communication connection network diagram of the intelligent connected workshop provided in an embodiment of the present application;

[0089] Figure 2 A position error diagram of a virtual signal and a leading connected vehicle provided in an embodiment of the present application;

[0090] Figure 3 A speed error diagram of a virtual signal and a leading connected vehicle provided in an embodiment of the present application;

[0091] Figure 4 The virtual signal provided in the embodiment of the present application and the acceleration error diagram of the leading connected vehicle;

[0092] Figure 5 A tracking position error diagram provided by an embodiment of the present application;

[0093] Figure 6 Tracking speed error diagram provided by the embodiment of the present application;

[0094] Figure 7 A tracking acceleration error diagram provided in an embodiment of the present application;

[0095] Figure 8 An event triggering timing diagram provided for an embodiment of the present application;

[0096] Figure 9 A cost function diagram provided for an embodiment of the present application. DETAILED DESCRIPTION

[0097] In order to make the objectives, technical solutions and advantages of this application clearer, the implementation methods of this application will be further described in detail below with reference to the accompanying drawings.

[0098] This application fully considers practical applications. The virtual reference layer integrates the resilience algorithm under attack and the distributed algorithm design, which can effectively resist the impact of DoS attacks and improve the security and stability of the system. The tracking control layer introduces the event trigger mechanism to the optimal control strategy, balances the relationship between limited communication computing resources and system performance optimization, and significantly improves system efficiency and performance.

[0099] Step 1: Build an intelligent connected vehicle system model; the intelligent connected vehicle system model includes a leading vehicle and a following vehicle;

[0100] The longitudinal dynamics equation of the i-th, i=1,2,...,N intelligent connected vehicles is described as:

[0101]

[0102] where p i represents the position of vehicle i, represents the speed of vehicle i, represents the acceleration of vehicle i, F i e represents the vehicle driving force, and the dynamic equation is expressed as:

[0103]

[0104] Where u i represents the throttle input of vehicle i, represents the component of gravity of vehicle i parallel to the road surface,

[0105] represents air resistance. Assuming that all vehicles are moving in the same direction, sig(v i +v w )=1. m represents the vehicle weight, represents the body resistance of vehicle i, g represents the acceleration due to gravity, represents the angle between the plane of the i-th vehicle and the road slope, m a Indicates the air density, S a represents the cross-sectional area of the vehicle, d c represents the air resistance coefficient, v w represents the wind speed, and T represents the inertia time of the power transmission system.

[0106] Let x i =[p i ,v i ,a i ] T is the state vector of the following connected vehicle, x0 is the nonlinear function of the leading connected vehicle, and f(x0) is the nonlinear function of the leading connected vehicle. is a nonlinear function following the connected car, is the external disturbance of the following connected vehicle, ω0 represents the external disturbance of the leader connected vehicle, and the system models of the leading vehicle and the following vehicle i are expressed as:

[0107]

[0108] and

[0109]

[0110] in and is the coefficient matrix, y i and y0 represent the output states of the following vehicle and the leading vehicle respectively, is the output matrix.

[0111] In the constructed intelligent connected vehicle system model, the state dynamic behavior is characterized by the system output state. Based on the output matrix C, the system output state has a coupling effect with the vehicle's position, velocity, and acceleration.

[0112] Step 2: Design a hierarchical optimal control method based on the mathematical model of the intelligent connected vehicle power system.

[0113] The hierarchical control method includes a virtual reference signal generation layer and a tracking control layer; the virtual reference layer signal generation layer integrates the resilience algorithm and distributed algorithm under attack to resist the impact of DoS attacks and improve the security and stability of the system; the tracking control layer introduces an event trigger mechanism into the optimal control strategy to balance the relationship between limited communication computing resources and system performance optimization, which can significantly improve system efficiency and performance.

[0114] Step 21: Construct a virtual reference signal generation layer

[0115] The purpose of the virtual reference layer is to design a virtual reference signal to ensure the fixed time consistency between the leader agent and the virtual signal under the influence of DoS attacks.

[0116] The DoS attack signal is defined as:

[0117]

[0118] Where k represents the number of attacks, t ak represents the time when the attack signal is activated, τ k Indicates the attack residence time, t a(k+1) Indicates the end time of the kth attack, A k =[t ak ,t k ),t k =t ak +τ k Indicates the attack range.

[0119] The virtual reference signal is designed as follows:

[0120]

[0121] where K1 and K2 are gain matrices of moderate dimensions, is the indicator function, ρ1 is a positive constant satisfying is a positive constant, V1 is the Lyapunov function designed to determine the stability of the implementation; a ij Is the adjacency matrix A=(a ij )∈R N×N The element of a ij >0 means that the following connected vehicle i can obtain status information from the following connected vehicle j, otherwise a ij =0;N i represents the set of connected vehicles that have communication connections with the i-th connected vehicle; d i Indicates the communication connection between the i-th follower connected car and the leader connected car. When the leader and the i-th follower connected car are connected, d i >0, otherwise d i =0; represents the elements of the adjacency matrix under the attack signal, represents the communication connection between the leader and the i-th following connected vehicle under the attack signal.

[0122] Based on the reference signal, the estimated time for the reference signal to achieve fixed time consistency with the leading connected vehicle is calculated as:

[0123]

[0124] Where γ is the state convergence rate, ρ1 is a positive constant satisfying is a positive constant, T 21 yes The minimum positive solution, T 22 yes The minimum positive solution of A constant limiting the total duration of a DoS attack.

[0125] Step 22: Construct a tracking control layer. The tracking control layer is used to formulate an optimal control plan to ensure that the reference signal is tracked within a fixed time and to achieve optimal system comprehensive performance indicators.

[0126] Step 221, constructing a tracking error model;

[0127] Based on the designed virtual reference signal and the following connected vehicle dynamics model, the tracking error state is defined as e i =Cx i -Cζ i , the error model is:

[0128]

[0129] in

[0130]

[0131] Step 222, constructing a performance index function related to the error state and the control law;

[0132] Based on the set tracking error state e i , define the performance index function as:

[0133]

[0134] In the formula Meet L i (0,0)=0,P i >0 and Q i >0 is a symmetric positive definite matrix, allowing control u i ∈U(Ω) piecewise continuous, satisfying u i (0) = 0 and at the rest time T max Internally stabilized connected vehicle error system.

[0135] Step 223, define the Hamiltonian function and propose the general form of the optimal control law;

[0136] In order to explore the optimal control law for the multi-UAV error system to achieve stability, the Hamiltonian function is defined:

[0137]

[0138] in Represents the optimal value function V i (e i )About e i Find the partial derivative and transpose; the optimal value function is solved by Obtained, expressed as:

[0139]

[0140] Optimal control law for:

[0141]

[0142] Among them B T Represents the transpose of the coefficient matrix B of the connected vehicle system. C T represents the transpose of the connected vehicle system output matrix C. Step 224 , propose an event triggering rule and an event triggering optimal control law for achieving optimal control within a fixed time.

[0143] set up is the triggering time sequence of the i-th error state, s represents the s-th triggering time, is the observation error, Indicates the trigger time The tracking error value at in is the sth trigger interval of the ith error state. Under the event trigger mechanism, the event trigger optimal control law is expressed as:

[0144]

[0145] The triggering time sequence is determined by the following event triggering rules:

[0146]

[0147] Among them, 0<ω1<1 is a positive constant, λ max (Q i ) represents the matrix Q i The maximum eigenvalue of min (P i ) represents the matrix P i The minimum eigenvalue of min (Q i ) represents the matrix Q i The minimum eigenvalue, L ui yes The Lipschitz constant satisfied.

[0148] Step 3: Based on event-triggered optimal control, an online algorithm based on reinforcement learning is used to determine the weight vector to approximate the optimal control law.

[0149] Since it is impossible to accurately solve the value function to obtain the event-triggered optimal control law, an online algorithm based on reinforcement learning is proposed to approximate the optimal control law. The specific steps include the following:

[0150] Step 31, constructing an approximate value function of a judgment neural network;

[0151] The approximate value function and gradient of the judging neural network are expressed as:

[0152]

[0153] In the formula represents the weight vector, represents the activation function, is the number of neurons, ∈ i is the approximation error, and the upper bound is ∈ im .

[0154] Step 32, estimating the value function and proposing the corresponding optimal control law;

[0155] Since the weight vector W i Unknown, let the estimate be The value function is expressed as:

[0156]

[0157] in It is V i (e i ), and then the optimal control strategy can be obtained, which is expressed as:

[0158]

[0159] Based on the estimated value function and the event-triggered optimal control law, the estimate of the Hamiltonian function is expressed as:

[0160]

[0161] Step 33, define the weight error vector, Bellman function and error E i ;

[0162] Define the weight vector error separately Bellman error and function E i for

[0163]

[0164] in express In t l The residual function at time η il represents η i In t l The value at time t l For time series The elements satisfy 0≤t l ,...,t s <t,s>0.

[0165] Step 34, determine the weight vector update rule and pause time;

[0166] In order to accurately estimate the weight vector Learning law is α The update rule is

[0167]

[0168] Based on the fixed-time stability theory, the dwell time for the tracking error model to stabilize is:

[0169]

[0170] in is a constant, is a constant, r1 is a constant, is a positive constant, is a constant, Representation matrix

[0171] Y i =[η i1 ,η i2 ,...,η ir ], is a constant, and τ1 is a positive constant.

[0172] The following further illustrates this application with reference to specific simulations

[0173] Select parameter m = 1000kg, m a =1.3kg / m 3 , S a =3.1m 2 , d c =0.5, v w = 2m / s, T = 0.2s. The initial position of the leading vehicle is set to 15m. The initial positions of following vehicles 1-4 are 9m, 8m, 5m, and 2m respectively. The initial speed of all vehicles is 5m / s. The communication structure of the vehicle platoon is as follows Figure 1As shown. The initial positions of virtual vehicles 1-4 are set to 10m, 6m, 8m, and 9m respectively, and the initial speeds are 2m / s, 3m / s, 2m / s, and 4m / s respectively. The ideal distance between virtual vehicle $i$ and the leading vehicle is set to 2im. ρ1=1.5, K1=diag{3.05,2.053,1.97}, For the tracking controller, the cost function parameters are set as P1 = 0.19, P2 = 0.14, P3 = 0.12, P4 = 0.14, Q1 = 0.6061, Q2 = 0.4, Q3 = 0.3534, Q4 = 0.3788, Activation Function Learning law α = 0.95, ω1 = 0.26, L1 = 0.67, L2 = 0.95, L3 = 0.96, L4 = 0.95, r2 = 0.5. Under the above parameters, the calculated rest time is T2 = 7.05. Figure 2-4 The position, velocity and acceleration trajectory changes of the leading vehicle and the virtual vehicle under DoS attack are given respectively. According to the set controller parameters, the tracking pause time can be calculated as T max =8.6153, the error trajectory between the following vehicle and the virtual vehicle is as follows Figure 5-7 As shown. The triggering time sequence generated under the event triggering mechanism can be seen Figure 8 The cost function curve can be seen Figure 9 .

[0174] The above-described embodiments of the present application do not constitute a limitation on the scope of protection of the present application.

Claims

1. A fixed-time optimal control method for intelligent connected vehicles against DoS attacks based on a hierarchical structure, characterized by: The method comprises: Step 1: Build an intelligent connected vehicle system model; the intelligent connected vehicle system model includes a leading vehicle and a following vehicle; Step 2: Design a hierarchical optimal control method based on the mathematical model of the intelligent connected vehicle powertrain; The layers include a virtual reference signal generation layer and a tracking control layer. The virtual reference signal generation layer integrates attack resilience algorithms and distributed algorithms to resist the impact of DoS attacks. The tracking control layer introduces an event trigger mechanism into the optimal control strategy to balance the relationship between communication computing resources and system performance optimization. Step 3: Based on event-triggered optimal control, an online algorithm based on reinforcement learning is used to determine the weight vector to approximate the optimal control law.

2. The method according to claim 1, characterized in that Step 1: Build an intelligent connected vehicle system model; including: The longitudinal dynamics equation of the i-th, i=1,2,...,N intelligent connected vehicles is described as: where p i represents the position of vehicle i, represents the speed of vehicle i, represents the acceleration of vehicle i, represents the vehicle driving force, and the dynamic equation is expressed as: Where u i represents the throttle input of vehicle i, represents the component of gravity of vehicle i parallel to the road surface, represents air resistance. Assuming that all vehicles are moving in the same direction, sig(v i +v w )=1; m represents the vehicle weight, represents the body resistance of vehicle i, g represents the acceleration due to gravity, represents the angle between the plane of the i-th vehicle and the road slope, m a Indicates the air density, S a represents the cross-sectional area of the vehicle, d c represents the air resistance coefficient, v w represents the wind speed, T represents the inertia time of the power transmission system; Let x i =[p i ,v i ,a i ] T is the state vector of the following connected vehicle, x0 is the nonlinear function of the leading connected vehicle, and f(x0) is the nonlinear function of the leading connected vehicle. is a nonlinear function following the connected car, is the external disturbance of the following connected vehicle, ω0 represents the external disturbance of the leader connected vehicle, and the system models of the leading vehicle and the following vehicle i are expressed as: and in and is the coefficient matrix, y i and y0 represent the output states of the following vehicle and the leading vehicle respectively, is the output matrix.

3. The method according to claim 1, characterized in that Step 2: Design a hierarchical optimal control method based on the mathematical model of the intelligent connected vehicle powertrain, including: Step 21, constructing a virtual reference signal generation layer; Step 22: Construct a tracking control layer. The tracking control layer is used to formulate an optimal control plan to ensure that the reference signal is tracked within a fixed time and to achieve optimal system comprehensive performance indicators.

4. The method according to claim 3, characterized in that Step 21, constructing a virtual reference signal generation layer; including: The DoS attack signal is defined as: Where k represents the number of attacks, t ak represents the time when the attack signal is activated, τ k Indicates the attack residence time, t a(k+1) Indicates the end time of the kth attack, A k =[t ak ,t k ),t k =t ak +τ k Indicates the attack range; The virtual reference signal is designed as follows: where K1 and K2 are gain matrices of moderate dimensions, is the indicator function, ρ1 is a positive constant satisfying is a positive constant, V1 is the Lyapunov function designed to determine the stability of the implementation; a ij Is the adjacency matrix A=(a ij )∈R N×N The element of a ij >0 means that the following connected vehicle i can obtain status information from the following connected vehicle j, otherwise a ij =0;N i represents the set of connected vehicles that have communication connections with the i-th connected vehicle; d i Indicates the communication connection between the i-th follower connected car and the leader connected car. When the leader and the i-th follower connected car are connected, d i >0, otherwise d i =0; represents the elements of the adjacency matrix under the attack signal, represents the communication connection between the leader and the i-th following connected vehicle under the attack signal; Based on the reference signal, the time it takes for the reference signal to be consistent with the fixed time of the leading connected vehicle is calculated as: Where γ is the state convergence rate, ρ1 is a positive constant satisfying is a positive constant, T 21 yes The minimum positive solution, T 22 yes The minimum positive solution of A constant limiting the total duration of a DoS attack.

5. The method according to claim 3, characterized in that Step 22: Construct a tracking control layer. The tracking control layer is used to formulate an optimal control plan to ensure that the reference signal is tracked within a fixed time and the overall system performance index is optimized, including: Step 221, constructing a tracking error model; Based on the designed virtual reference signal and the following connected vehicle dynamics model, the tracking error state is defined as e i =Cx i -Cζ i , the error model is: in Step 222: Construct a performance index function related to the error state and the control law: Based on the set tracking error state e i , define the performance index function as: In the formula Meet L i (0,0)=0,P i >0 and Q i >0 is a symmetric positive definite matrix, allowing control u i ∈U(Ω) piecewise continuous, satisfying u i (0) = 0 and at the rest time T max Internally stabilize the error system of the connected vehicle; Step 223, define the Hamiltonian function and propose the general form of the optimal control law: Define the Hamiltonian function: in Represents the optimal value function V i (e i )About e i Find the partial derivative and transpose; the optimal value function is solved by Obtained, expressed as: Optimal control law for: Among them B T represents the transpose of the coefficient matrix B of the connected vehicle system; C T represents the transpose of the output matrix C of the connected vehicle system; Step 224: Propose event triggering rules and event triggering optimal control laws for achieving optimal control within a fixed time: set up is the triggering time sequence of the i-th error state, s represents the s-th triggering time, is the observation error, Indicates the trigger time The tracking error value at in is the sth trigger interval of the ith error state. Under the event trigger mechanism, the event trigger optimal control law is expressed as: The triggering time sequence is determined by the following event triggering rules: Among them, 0<ω1<1 is a positive constant, λ max (Q i ) represents the matrix Q i The maximum eigenvalue of min (P i ) represents the matrix P i The minimum eigenvalue of min (Q i ) represents the matrix Q i The minimum eigenvalue, L ui yes The Lipschitz constant satisfied.

6. The method according to claim 1, characterized in that Step 3: Based on event-triggered optimal control, an online algorithm based on reinforcement learning is used to determine the weight vector to approximate the optimal control law. include: Step 31, constructing an approximate value function of a judgment neural network; Step 32, estimating the value function and proposing the corresponding optimal control law; Step 33, define the weight error vector, Bellman function and error E i ; Step 34: Determine the weight vector update rule and pause time.

7. The method according to claim 6, characterized in that Step 31, constructing a judgment neural network approximation function; including: The approximate value function and gradient of the judging neural network are expressed as: In the formula represents the weight vector, represents the activation function, is the number of neurons, ∈ i is the approximation error, and the upper bound is ∈ im .

8. The method according to claim 6, characterized in that Step 32, estimating the value function and proposing the corresponding optimal control law, includes: Since the weight vector W i Unknown, let the estimate be The value function is expressed as: in It is V i (e i ), and then the optimal control strategy can be obtained, which is expressed as: Based on the estimated value function and the event-triggered optimal control law, the estimate of the Hamiltonian function is expressed as:

9. The method according to claim 6, characterized in that Step 33, define the weight error vector, Bellman function and error E i ; include: Define the weight vector error separately Bellman error and function E i for in express In t l The residual function at time η il represents η i In t l The value at time t l For time series The elements satisfy 0≤t l ,...,t s <t,s>0.

10. The method according to claim 6, characterized in that Step 34, determining the weight vector update rule and pause time, including: In order to accurately estimate the weight vector Learning law is α The update rule is Based on the fixed-time stability theory, the dwell time for the tracking error model to stabilize is: where θ 3i =min{θ1,θ 2i }m4 is a constant, is a constant, r1 is a constant, is a positive constant, is a constant, Represents the matrix Y i =[η i1 ,η i2 ,...,η ir ], is a constant, and τ1 is a positive constant.

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