Automobile queue control method based on pipeline distributed model predictive control

Abstract

The invention discloses an automobile queue control method based on pipeline distributed model predictive control, and belongs to the field of intelligent automobiles and intelligent traffic. The method comprises the following steps: constructing a vehicle discrete dynamic model; establishing a queue cooperative control framework through vehicle-vehicle communication; introducing a wheel slip rate into the queue performance index function, and setting a longitudinal slip rate as a constraint; on the basis of nominal model predictive control, a nominal optimal control input sequence and an optimal state track are generated through decision making; and then the state of the disturbed vehicle is corrected in real time through an auxiliary control law, so that the disturbed vehicle is restrained near the optimal track. In the queue car-following control process, an interference suppression mechanism and tire nonlinear modeling are introduced into the system, and the limitation that the node vehicle stability and the full-queue control performance are not sufficiently considered in a traditional method is broken through. Even under the limiting working conditions of high-speed driving, low adhesion and the like, the stability and the good all-working-condition control performance of the automobile queue can be guaranteed.

Description

Technical Field

[0001] The present invention relates to the fields of smart cars and smart transportation, and in particular to a car queue control method based on pipeline distributed model predictive control. Background Art

[0002] With the development of autonomous driving and in-vehicle communication technologies, connected autonomous vehicles (CAVs) are attracting increasing attention due to their potential to improve traffic efficiency and safety. Platooning is a key implementation method for CAVs within intelligent transportation systems. Platooning involves vehicles acquiring information about the vehicle ahead through onboard sensors or communications, then making decisions based on this information to maintain a predetermined distance between them and the vehicle ahead. Platooning has significant potential to reduce energy consumption, increase traffic flow, alleviate congestion, and improve traffic safety.

[0003] However, under low-adhesion road conditions, when platooning vehicles experience rapid acceleration or deceleration, wheel slip increases significantly, tire forces enter a highly nonlinear or even saturated region, and the vehicle transitions from a linear to a highly nonlinear control domain. This makes dynamic behavior extremely complex, making it difficult for traditional control strategies to effectively address this issue. This leads to a significant decline in car-following control performance, and in severe cases, can lead to rear-end collisions within the platoon. Furthermore, in real-world driving environments, vehicles are inevitably affected by the combined effects of modeling errors and external disturbances (such as wind, slope changes, and road surface irregularities), further increasing the challenges of platooning control. Therefore, existing platooning control methods urgently need to systematically incorporate comprehensive considerations of tire force nonlinearity, modeling errors, and external disturbances into their control strategy design to ensure both the dynamic stability of node vehicles and the overall stability of the platoon system, and to achieve efficient and reliable car-following control even under extreme conditions. This issue has become a major technical challenge that needs to be addressed in the field of autonomous vehicle platooning control. Summary of the Invention

[0004] In view of the above problems, the object of the present invention is to provide a vehicle platoon control method based on pipeline distributed model predictive control.

[0005] To achieve the above purpose, the steps are as follows:

[0006] S1. Based on longitudinal dynamics, a nodal vehicle model including nonlinear tire forces and wheel rotational dynamics is constructed by introducing the magic formula, normal force calculation, slip rate and rotational dynamics equations;

[0007] The build steps are as follows:

[0008] S1.1. Define the longitudinal dynamic equation of the vehicle after disturbance, as follows:

[0009]

[0010] Where, is the longitudinal acceleration of vehicle i; m i is the mass of vehicle i; F xfi (t) and F xri (t) are the longitudinal tire forces on the front and rear wheels of vehicle i; g is the acceleration due to gravity; f r is the rolling resistance coefficient; i (t) is the acceleration disturbance caused by external disturbance and modeling error;

[0011] S1.2. The longitudinal tire force of the vehicle is modeled based on the magic formula tire force model to reflect nonlinear tire forces. The expression is as follows:

[0012] F xji (t) = μD xji (t)sin(C x arctan(B xji (t)Φ xji (t)))

[0013]

[0014] Φ xji (t) = (1-E xji (t))δ xji (t)+(E xji (t) / B xji (t))arctan(B xji (t)δ xji (t));

[0015]

[0016] Where, j = f, r, when j is f, it is the front wheel, when j is r, it is the rear wheel; μ is the road adhesion coefficient; C x is the coefficient term, C x =1.65; α1~α8 are the first to eighth constant terms; e is the base of natural logarithm; F zji (t) is the normal force of wheel j; δ xji (t) is the longitudinal slip rate of wheel j;

[0017] S1.3. Considering the effect of vehicle acceleration on tire loads, calculate the normal forces on the front and rear wheels using the following expressions:

[0018]

[0019] Where a i (t) is the longitudinal acceleration of vehicle i, let hc is the height of the vehicle's center of mass; l f and l r are the horizontal distances from the center of mass to the front and rear axles of the vehicle respectively; l is the wheelbase of the vehicle and l=l f +l r ;

[0020] S1.4. Calculate the longitudinal slip of wheel j to distinguish between acceleration and braking conditions. The expression is as follows:

[0021]

[0022] Where r wi is the tire radius of vehicle i; v i (t) is the vehicle speed; ω wji (t) is the rotational angular velocity of wheel j;

[0023] S1.5. Calculate the wheel angular velocity using the rotational dynamics equation. The expression is as follows:

[0024]

[0025] Where, I w is the moment of inertia; is the derivative of the angular velocity of wheel j; T wji (t) is the torque applied to wheel j; F xji (t) is the longitudinal force of wheel j;

[0026] S1.6. Based on S1.4, the longitudinal slip derivative of wheel j during acceleration and deceleration can be obtained as follows:

[0027]

[0028] Where, is the derivative of the longitudinal slip rate of wheel j;

[0029] S1.7. Substitute S1.1 and S1.5 into S1.6 to eliminate the derivative term. The expression is as follows:

[0030]

[0031] S2. Linearize the nonlinear tire forces of the vehicle, use the recursive least squares method to estimate the slip slope and calculate the longitudinal stiffness of the wheel, the steps are as follows:

[0032] S2.1. On low-adhesion roads, the tire force of a vehicle is expressed as follows:

[0033] F xji (t) = k xji (t)δ xji(t), j = f, r

[0034] Where k xji (t) is the longitudinal stiffness of wheel j; let in, The coefficient used to describe the difference between the front tire stiffness and the rear tire stiffness when the vehicle is in all-wheel traction or braking conditions. Then the vehicle is rear-wheel drive or braked;

[0035] S2.2 The relationship between tire longitudinal force and slip is expressed as follows:

[0036]

[0037] Where, F xi (t) is the sum of the longitudinal tire forces of the vehicle, F xi (t) = F xfi (t)+F xri (t); k ri (t) is the estimated slip slope; is the regression vector;

[0038] S2.3. Based on S2.2, the recursive least squares method is used to estimate the vehicle slip slope, which is expressed as follows:

[0039]

[0040] Where θ i (t) is the estimated slip slope, corresponding to θ in S2.2 i (t) = k ri Part (t); is the estimated regression vector, corresponding to S2.2 Part; y i (t) is the estimated longitudinal tire force of the vehicle, corresponding to F in S2.2 xi Part (t);

[0041] S2.4. Based on S2.3, calculate the estimated error using the estimated output. The estimated error is the difference between the current actual output and the estimated output predicted at the previous moment. The expression is as follows:

[0042]

[0043] Where, e fi (t) is the estimation error; θ i (t-1) is the estimated slip slope at the previous moment;

[0044] S2.5. Construct the gain vector and covariance matrix. The calculation method is as follows:

[0045]

[0046] Where K i (t) is the gain vector; P i (t) is the covariance matrix; P i (t-1) is the covariance matrix of the previous moment; λ1 is the forgetting factor, 0.9≤λ i ≤1;

[0047] S2.6. Update the estimated vehicle slip slope, expressed as:

[0048] θ i (t) = θ i (t-1)+K i (t)e fi (t);

[0049] S2.7. Calculate the vehicle longitudinal stiffness based on the updated vehicle slip slope estimate using the following expression:

[0050]

[0051] k xri (t) = k ri (t)F zri (t).

[0052] S3. Based on S1 and S2, a discrete model of a single node vehicle model is constructed. The steps are as follows:

[0053] S3.1. Based on removing the last item of S1.1, that is, removing the influence of acceleration interference caused by external disturbances and modeling errors, construct the nominal discretization model of the node vehicle in S1.5, S1.7, and S2.1. The expression is as follows:

[0054]

[0055] Where, f i z is the gradient of the nominal state variable of the system at time t; Δt is the discrete time; is the nominal state variable of vehicle node i, where is the nominal position of vehicle i, is the nominal longitudinal velocity of vehicle i, and are the nominal longitudinal slip rates of the front and rear wheels of vehicle i, respectively; is the system nominal input, and are the nominal torques for the front and rear wheels, respectively;

[0056] S3.2. Based on S3.1, calculate the nominal state variable of vehicle node i. The expression is as follows:

[0057]

[0058] Where, and are the nominal positions of vehicle i at time t+1 and time t, respectively; and are the nominal longitudinal velocities of vehicle i at time t+1 and time t, respectively; and are the nominal longitudinal slip rates of wheel j at time t+1 and time t, respectively; is time t The gradient of change; is time t The gradient of change;

[0059] S3.3. Calculate the discretization of wheel speed. The expression is as follows:

[0060]

[0061] Where, and are the nominal rotational angular velocities of wheel j at time t+1 and time t, respectively; for The gradient of change at time t.

[0062] S4. Based on the discrete model constructed in S3, calculate the node vehicle state sequence and send the state sequence of the vehicle to the following vehicle and receive the state sequence of the leading vehicle to construct a platoon control model. The steps are as follows:

[0063] S4.1. The vehicles in the queue adopt a timed distance formation strategy, and the expected distance d of vehicle i i (t) is expressed as follows:

[0064]

[0065] Where, d sta is the safe distance when the vehicle is stationary; h w is the headway; is the speed of vehicle i;

[0066] S4.2. Calculate the vehicle following distance error using the following expression:

[0067]

[0068] Where p i-1 (t) and p i (t) are the positions of vehicle i and vehicle i-1 respectively; is the speed of vehicle i during car-following;

[0069] S4.3. The motion state sequence of the preceding vehicle is obtained through vehicle-to-vehicle communication. The expression of the platoon control model is as follows:

[0070]

[0071] Where, and denote the first matrix and the second matrix respectively, is the nominal state variable of the queue control model; Nominal state variables of vehicle i-1 node; is the nominal state variable of vehicle node i;

[0072] S4.4. Based on S3.1, the vehicle state at the next moment needs to be predicted based on the vehicle state at the current moment and the control input. The platoon control model in S4.3 is organized and constraints are set. The expression is:

[0073]

[0074] Where, is the nominal state variable of the control model, where f i is a nonlinear function determined by the nodal vehicle dynamics model;

[0075] The queue control model is constrained by state variables and control inputs, and is expressed as follows:

[0076]

[0077] Where, is the state constraint set; is the input constraint set.

[0078] S5. Set the nominal performance index function and auxiliary performance index function of the platoon vehicles, and use the wheel longitudinal slip rate as a constraint. The steps are as follows:

[0079] S5.1. At time t, after constructing the local nominal optimal control problem expression for vehicle i and setting the cost function, construct the cost function of the local nominal optimal control problem expression for vehicle i;

[0080] The optimal control problem is as follows:

[0081]

[0082] Where, The nominal predicted state sequence of the control model for vehicle i; The nominal forecast input sequence for the control model of vehicle i; is the nominal assumed state sequence of the control model for vehicle i-1; and They are the 0th and kth steps at time t respectively p1 -1 step vehicle i control model nominal prediction input, k p1 is the nominal forecast horizon;

[0083] The expression to set the constraint is as follows:

[0084]

[0085] Where, and are the nominal predicted state and nominal predicted input of the control model of vehicle i at the kth step at time t, respectively; and are the nominal predicted states of the control model of vehicle i at time t, step k+1 and step 0 respectively; x i (t) is the measured value of the state variable of the control model at time t; is the terminal set;

[0086] The cost function of the local nominal optimal control problem expression for vehicle i is as follows:

[0087]

[0088] Where, is the nominal assumed state of the control model of vehicle i-1 at time t, step k; is the nominal state weight matrix of the control model; Enter the weight matrix for nominal control; is the weight matrix of the following vehicle; is the terminal constraint matrix;

[0089] S5.2. At time t, after constructing the local auxiliary optimal control problem expression for vehicle i and setting constraints, construct a cost function for the local auxiliary optimal control problem expression for vehicle i;

[0090] The local auxiliary optimal control problem of vehicle i is expressed as follows:

[0091]

[0092] Where, is the nominal optimal state sequence; x i The control model predicts the state sequence for vehicle i; u i Predict the input sequence for the control model of vehicle i; u i (0|t) and u i (kp2 -1|t) are the 0th and kth steps at time t respectively p2 -1 step vehicle i control model prediction input, k p2 Predicting the time domain for auxiliary control;

[0093] The expression to set the constraint is as follows:

[0094] x i (k+1|t)=f i (x i (k|t),u i (k|t))

[0095] s i (k+1|t)=s i (k|t)+λ i (k|t)Δt

[0096]

[0097] x i (k|t)∈X i ,u i (k|t)∈U i

[0098] x i (k p2 |t)∈X fi

[0099] Where x i (k+1|t) is the predicted state of the auxiliary controller at the k+1th step at time t; x i (k|t) is the predicted state at time t, step k; u i (k|t) is the predicted input of the auxiliary controller at time t, step k; s i (k+1|t) and s i (k|t) are the pipeline sizes of the k+1th step and the kth step at time t; λ i (k|t) is the pipeline change rate at step k at time t; and are the upper bound of the pipeline at the kth step at time t and the upper bound of the pipeline change rate; O i is the weight coefficient matrix describing the pipe shape; ν i (k|t) is the tightening constraint coefficient of the kth step at time t; in and are the Lipschitz coefficients corresponding to external interference and state error, is the norm of the upper bound of external interference; X i and U iare auxiliary controller state constraints and control input constraints respectively, X fi Auxiliary control terminal set;

[0100] The cost function of the local auxiliary optimal control problem expression of vehicle i is as follows:

[0101]

[0102] Where, is the nominal optimal predicted state of the vehicle i control model at time t, step k, x i (k|t) and u i (k|t) are the predicted state and predicted input of the control model of vehicle i at the kth step at time t, S i (k|t) is the pipeline size and pipeline change rate at the kth step at time t, S i (k|t)=[s i (k|t),λ i (k|t)] T where s i (k|t) and λ i (k|t) are the pipeline size and pipeline change rate of the kth step at time t, Q i To control the auxiliary state weight matrix of the model, R i Input weight matrix for auxiliary control, P i is the pipeline weight matrix.

[0103] S6. Solve the nominal performance index function set in step S5 to calculate a nominal optimal control sequence; construct a nominal hypothetical input sequence and a nominal hypothetical state sequence and transmit them to the following vehicle; calculate the nominal optimal state sequence using the nominal optimal control sequence and solve the auxiliary performance index function; apply the first element of the optimal control input of the solved auxiliary performance index function to the vehicle, completing full-condition control of the vehicle platoon;

[0104] Here are the steps:

[0105] S6.1. Perform initialization operations. The steps are as follows:

[0106] First, calculate offline the terminal elements The corresponding matrix of For terminal sets, is the terminal control law, is the terminal cost function; suppose there exists a matrix Make Stable, and The Jacobian matrix of the queue control model after the arrangement in step S4.4 is the state matrix and the input matrix respectively. Let where β i >1, is a symmetric positive semidefinite matrix and is The solution, and select the appropriate external interference and the Lipschitz coefficient corresponding to the state error and And the norm of the upper bound of external interference

[0107] When the speeds of all vehicles in the queue are equal and the acceleration inputs of the vehicles are all 0, the elements in the hypothetical input sequence of vehicle i and the hypothetical input sequence of vehicle i-1 are all inputs when the vehicles are in equilibrium. wji =F zji f r r wi , the corresponding assumed vehicle state and predicted vehicle state are calculated through the discrete vehicle model. The expression is as follows:

[0108]

[0109] Where, and are the nominal assumed state variables and nominal predicted state variables of vehicle i at step k at time 0, and are the nominal assumed state variables and nominal predicted state variables of the vehicle i-1 node at time 0, step k, respectively;

[0110] and The calculation process is as follows:

[0111]

[0112] Where, and are the nominal predicted state variables of vehicle i at time 0, step 0, step k, and step k+1, respectively. is the nominal hypothesis input of the kth step at time 0, is the nominal predicted state of the vehicle i control model at time 0, step k, is the nominal assumed state variable of vehicle i at step k at time 0, z i (0) is the measured value of the state variable of vehicle i node at the current moment;

[0113] S6.2: At any time t, solve the nominal optimization problem S5.1 of the control model for vehicle i to obtain the nominal optimal predictive control input sequence k=0,…,k p1 -1;

[0114] S6.3: Pass Calculate the nominal optimal state sequence at the current moment And the nominal optimal state sequence of the control model k=0,…,k p1 -1, the specific expression is as follows:

[0115]

[0116] Where, and are the nominal assumed state variables of vehicle i at step 0, step k and step k+1 at time t+1, is the nominal hypothesis input for the kth step at time t+1, is the nominal assumed state of the vehicle i control model at the kth step at time t+1, is the nominal assumed state variable of vehicle i at step k at time t+1, is the nominal optimal state variable of vehicle i node in the first step at time t;

[0117] S6.5: Apply the first control variable u of the auxiliary optimal predictive control input sequence obtained by solving the optimization problem on vehicle i i (0|t);

[0118] S6.6: Calculate the nominal hypothetical input sequence for the next step. Shift the nominal optimal control sequence at time t to the left, except for the first control input. Assume that the predicted terminal control input is the relationship between the terminal control law and the terminal state. Obtain the corresponding hypothetical output sequence, which is expressed as follows:

[0119]

[0120] Where, is the nominal hypothesis input for the kth step at time t+1, is the nominal optimal control input for the k+1th step at time t, is the nominal optimal state of the vehicle i control model at time t, is the terminal control law;

[0121] Accordingly, the vehicle state calculation formula is as follows:

[0122]

[0123] Where: and are the nominal assumed state variables of vehicle i at step 0, step k and step k+1 at time t+1, is the nominal hypothesis input for the kth step at time t+1, is the nominal assumed state of the vehicle i control model at the kth step at time t+1, is the nominal assumed state variable of vehicle i at step k at time t+1, is the nominal optimal state variable of vehicle i node in the first step at time t;

[0124] S6.7: Receive the nominal assumed vehicle state sequence of the preceding vehicle through vehicle-to-vehicle communication Construct a control model and Assume that the control sequence Send to the following vehicle;

[0125] S6.8: Return to step S6.2 to implement rolling time domain control.

[0126] Beneficial effects of the present invention:

[0127] (1) This invention addresses the problem that traditional platoon control methods ignore the effects of tire nonlinear dynamics and external disturbances. The system introduces a nonlinear saturation modeling and disturbance suppression mechanism for tire forces. Even under complex operating conditions such as model parameter uncertainty, strong disturbances, high-speed operation, and low adhesion limits, it effectively ensures the stability and following performance of the platoon, significantly improving the control system's ability to adapt to extreme operating conditions.

[0128] (2) By incorporating the dynamic characteristics of tire slip rate into the platoon following performance index function, compared with the limitations of traditional platoon control strategies that are only based on vehicle kinematics or simplified dynamic models, the present invention achieves active protection of node vehicle stability at the dynamic level and improves the robustness of the controller to parameter changes and external disturbances.

[0129] (3) During the platoon following control process, the present invention uses the wheel slip rate as an important state constraint and combines it with the real-time optimized pipe size and pipe change rate strategy to achieve excellent control effects under different working conditions such as high-adhesion and low-adhesion road surfaces, thereby having good adaptability to working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] Figure 1 is a flow chart of the present invention;

[0131] Figure 2 Schematic diagram of autonomous vehicle platoon;

[0132] Figure 3 The full-operation control process architecture of the autonomous vehicle platoon based on pipeline distributed model predictive control provided by the present invention;

[0133] Figure 4 is the following distance error curve of the vehicle platoon under high adhesion conditions;

[0134] Figure 5is the acceleration curve of the vehicle platoon under high adhesion conditions;

[0135] Figure 6 is the slip rate curve of the vehicle platoon under high adhesion conditions;

[0136] Figure 7 is the following distance error curve of the vehicle platoon under low adhesion conditions;

[0137] Figure 8 is the acceleration curve of the vehicle platoon under low adhesion conditions;

[0138] Figure 9 is the slip rate curve of the vehicle platoon under low adhesion conditions. DETAILED DESCRIPTION

[0139] The present invention is further described in detail below with reference to specific embodiments.

[0140] like Figure 1 As shown in the figure, a vehicle platoon control method based on pipeline distributed model predictive control is proposed for Figure 2 The control flow architecture of the autonomous vehicle platoon shown is as follows Figure 3 As shown, the steps are as follows:

[0141] S1. Based on longitudinal dynamics, a nodal vehicle model including nonlinear tire forces and wheel rotational dynamics is constructed by introducing the magic formula, normal force calculation, slip rate and rotational dynamics equations;

[0142] The build steps are as follows:

[0143] S1.1. Define the longitudinal dynamic equation of the vehicle after disturbance, as follows:

[0144]

[0145] Where, is the longitudinal acceleration of vehicle i; m i is the mass of vehicle i; F xfi (t) and F xri (t) are the longitudinal tire forces on the front and rear wheels of vehicle i; g is the acceleration due to gravity; f r is the rolling resistance coefficient; i (t) is the acceleration disturbance caused by external disturbance and modeling error;

[0146] S1.2. The longitudinal tire force of the vehicle is modeled based on the magic formula tire force model to reflect nonlinear tire forces. The expression is as follows:

[0147] F xji (t) = μD xji (t)sin(C xarctan(B xji (t)Φ xji (t)))

[0148]

[0149] Φ xji (t) = (1-E xji (t))δ xji (t)+(E xji (t) / B xji (t))arctan(B xji (t)δ xji (t));

[0150]

[0151] Where, j = f, r, when j is f, it is the front wheel, when j is r, it is the rear wheel; μ is the road adhesion coefficient; C x is the coefficient term, C x =1.65; α1~α8 are the first to eighth constant terms; e is the base of natural logarithm; F zji (t) is the normal force of wheel j; δ xji (t) is the longitudinal slip rate of wheel j;

[0152] S1.3. Considering the effect of vehicle acceleration on tire loads, calculate the normal forces on the front and rear wheels using the following expressions:

[0153]

[0154] Where a i (t) is the longitudinal acceleration of vehicle i, let h c is the height of the vehicle's center of mass; l f and l r are the horizontal distances from the center of mass to the front and rear axles of the vehicle respectively; l is the wheelbase of the vehicle and l=l f +l r ;

[0155] S1.4. Calculate the longitudinal slip of wheel j to distinguish between acceleration and braking conditions. The expression is as follows:

[0156]

[0157] Where r wi is the tire radius of vehicle i; v i (t) is the vehicle speed; ω wji (t) is the rotational angular velocity of wheel j;

[0158] S1.5. Calculate the wheel angular velocity using the rotational dynamics equation. The expression is as follows:

[0159]

[0160] Where, I w is the moment of inertia; is the derivative of the angular velocity of wheel j; T wji (t) is the torque applied to wheel j; F xji (t) is the longitudinal force of wheel j;

[0161] S1.6. Based on S1.4, the longitudinal slip derivative of wheel j during acceleration and deceleration can be obtained as follows:

[0162]

[0163] Where, is the derivative of the longitudinal slip rate of wheel j;

[0164] S1.7. Substitute S1.1 and S1.5 into S1.6 to eliminate the derivative term. The expression is as follows:

[0165]

[0166] S2. Linearize the nonlinear tire forces of the vehicle, use the recursive least squares method to estimate the slip slope and calculate the longitudinal stiffness of the wheel, the steps are as follows:

[0167] S2.1. On low-adhesion roads, the tire force of a vehicle is expressed as follows:

[0168] F xji (t) = k xji (t)δ xji (t), j = f, r

[0169] Where k xji (t) is the longitudinal stiffness of wheel j; let in, The coefficient used to describe the difference between the front tire stiffness and the rear tire stiffness when the vehicle is in all-wheel traction or braking conditions. Then the vehicle is rear-wheel drive or braked;

[0170] S2.2 The relationship between tire longitudinal force and slip is expressed as follows:

[0171]

[0172] Where, F xi (t) is the sum of the longitudinal tire forces of the vehicle, F xi (t) = F xfi (t)+Fxri (t); k ri (t) is the estimated slip slope; is the regression vector;

[0173] S2.3. Based on S2.2, the recursive least squares method is used to estimate the vehicle slip slope, which is expressed as follows:

[0174]

[0175] Where θ i (t) is the estimated slip slope, corresponding to θ in S2.2 i (t) = k ri Part (t); is the estimated regression vector, corresponding to S2.2 Part; y i (t) is the estimated longitudinal tire force of the vehicle, corresponding to F in S2.2 xi Part (t);

[0176] S2.4. Based on S2.3, calculate the estimated error using the estimated output. The estimated error is the difference between the current actual output and the estimated output predicted at the previous moment. The expression is as follows:

[0177]

[0178] Where, e fi (t) is the estimation error; θ i (t-1) is the estimated slip slope at the previous moment;

[0179] S2.5. Construct the gain vector and covariance matrix. The calculation method is as follows:

[0180]

[0181]

[0182] Where K i (t) is the gain vector; P i (t) is the covariance matrix; P i (t-1) is the covariance matrix of the previous moment; λ1 is the forgetting factor, 0.9≤λ i ≤1;

[0183] S2.6. Update the estimated vehicle slip slope, expressed as:

[0184] θ i (t) = θ i (t-1)+K i (t)e fi (t);

[0185] S2.7. Calculate the vehicle longitudinal stiffness based on the updated vehicle slip slope estimate using the following expression:

[0186]

[0187] k xri (t) = k ri (t)F zri (t).

[0188] S3. Based on S1 and S2, a discrete model of a single node vehicle model is constructed. The steps are as follows:

[0189] S3.1. Based on removing the last item of S1.1, that is, removing the influence of acceleration interference caused by external disturbances and modeling errors, construct the nominal discretization model of the node vehicle in S1.5, S1.7, and S2.1. The expression is as follows:

[0190]

[0191] Where, f i z is the gradient of the nominal state variable of the system at time t; Δt is the discrete time; is the nominal state variable of vehicle node i, where is the nominal position of vehicle i, is the nominal longitudinal velocity of vehicle i, and are the nominal longitudinal slip rates of the front and rear wheels of vehicle i, respectively; is the system nominal input, and are the nominal torques for the front and rear wheels, respectively;

[0192] S3.2. Based on S3.1, calculate the nominal state variable of vehicle node i. The expression is as follows:

[0193]

[0194] Where, and are the nominal positions of vehicle i at time t+1 and time t, respectively; and are the nominal longitudinal velocities of vehicle i at time t+1 and time t, respectively; and are the nominal longitudinal slip rates of wheel j at time t+1 and time t, respectively; is time t The gradient of change; is time t The gradient of change;

[0195] S3.3. Calculate the discretization of wheel speed. The expression is as follows:

[0196]

[0197] Where, and are the nominal rotational angular velocities of wheel j at time t+1 and time t, respectively; for The gradient of change at time t.

[0198] S4. Based on the discrete model constructed in S3, calculate the node vehicle state sequence and send the state sequence of the vehicle to the following vehicle and receive the state sequence of the leading vehicle to construct a platoon control model. The steps are as follows:

[0199] S4.1. The vehicles in the queue adopt a timed distance formation strategy, and the expected distance d of vehicle i i (t) is expressed as follows:

[0200]

[0201] Where, d sta is the safe distance when the vehicle is stationary; h w is the headway; is the speed of vehicle i;

[0202] S4.2. Calculate the vehicle following distance error using the following expression:

[0203]

[0204] Where p i-1 (t) and p i (t) are the positions of vehicle i and vehicle i-1 respectively; is the speed of vehicle i during car-following;

[0205] S4.3. The motion state sequence of the preceding vehicle is obtained through vehicle-to-vehicle communication. The expression of the platoon control model is as follows:

[0206]

[0207] Where, and denote the first matrix and the second matrix respectively, is the nominal state variable of the queue control model; Nominal state variables of vehicle i-1 node; is the nominal state variable of vehicle node i;

[0208] S4.4. Based on S3.1, the vehicle state at the next moment needs to be predicted based on the vehicle state at the current moment and the control input. The platoon control model in S4.3 is organized and constraints are set. The expression is:

[0209]

[0210] Where, is the nominal state variable of the control model, where f i is a nonlinear function determined by the nodal vehicle dynamics model;

[0211] The queue control model is constrained by state variables and control inputs, and is expressed as follows:

[0212]

[0213] Where, is the state constraint set; is the input constraint set.

[0214] S5. Set the nominal performance index function and auxiliary performance index function of the platoon vehicles, and use the wheel longitudinal slip rate as a constraint. The steps are as follows:

[0215] S5.1. At time t, after constructing the local nominal optimal control problem expression for vehicle i and setting the cost function, construct the cost function of the local nominal optimal control problem expression for vehicle i;

[0216] The optimal control problem is as follows:

[0217]

[0218] Where, The nominal predicted state sequence of the control model for vehicle i; The nominal forecast input sequence for the control model of vehicle i; is the nominal assumed state sequence of the control model for vehicle i-1; and They are the 0th and kth steps at time t respectively p1 -1 step vehicle i control model nominal prediction input, k p1 is the nominal forecast horizon;

[0219] The expression to set the constraint is as follows:

[0220]

[0221] Where, and are the nominal predicted state and nominal predicted input of the control model of vehicle i at the kth step at time t, respectively; and are the nominal predicted states of the control model of vehicle i at time t, step k+1 and step 0 respectively; x i (t) is the measured value of the state variable of the control model at time t; is the terminal set;

[0222] The cost function of the local nominal optimal control problem expression for vehicle i is as follows:

[0223]

[0224] Where, is the nominal assumed state of the control model of vehicle i-1 at time t, step k; is the nominal state weight matrix of the control model; Enter the weight matrix for nominal control; is the weight matrix of the following vehicle; is the terminal constraint matrix;

[0225] S5.2. At time t, after constructing the local auxiliary optimal control problem expression for vehicle i and setting constraints, construct a cost function for the local auxiliary optimal control problem expression for vehicle i;

[0226] The local auxiliary optimal control problem of vehicle i is expressed as follows:

[0227]

[0228] Where, is the nominal optimal state sequence; x i The control model predicts the state sequence for vehicle i; u i Predict the input sequence for the control model of vehicle i; u i (0|t) and u i (k p2 -1|t) are the 0th and kth steps at time t respectively p2 -1 step vehicle i control model prediction input, k p2 Predicting the time domain for auxiliary control;

[0229] The expression to set the constraint is as follows:

[0230] x i (k+1|t)=f i (x i (k|t),u i (k|t))

[0231] s i (k+1|t)=s i (k|t)+λ i (k|t)Δt

[0232]

[0233] x i (k|t)∈X i ,u i (k|t)∈U i

[0234] x i (k p2 |t)∈X fi

[0235] Where x i (k+1|t) is the predicted state of the auxiliary controller at the k+1th step at time t; x i (k|t) is the predicted state at time t, step k; u i (k|t) is the predicted input of the auxiliary controller at time t, step k; s i (k+1|t) and s i (k|t) are the pipeline sizes of the k+1th step and the kth step at time t; λ i (k|t) is the pipeline change rate at step k at time t; and are the upper bound of the pipeline at the kth step at time t and the upper bound of the pipeline change rate; O i is the weight coefficient matrix describing the pipe shape; ν i (k|t) is the tightening constraint coefficient of the kth step at time t; in and are the Lipschitz coefficients corresponding to external interference and state error, is the norm of the upper bound of external interference; X i and U i are auxiliary controller state constraints and control input constraints respectively, X fi Auxiliary control terminal set;

[0236] The cost function of the local auxiliary optimal control problem expression of vehicle i is as follows:

[0237]

[0238] Where, is the nominal optimal predicted state of the vehicle i control model at the kth step at time t, x i (k|t) and u i (k|t) are the predicted state and predicted input of the control model of vehicle i at the kth step at time t, S i (k|t) is the pipeline size and pipeline change rate at the kth step at time t, S i (k|t)=[si (k|t),λ i (k|t)] T where s i (k|t) and λ i (k|t) are the pipeline size and pipeline change rate of the kth step at time t, Q i To control the auxiliary state weight matrix of the model, R i Input weight matrix for auxiliary control, P i is the pipeline weight matrix.

[0239] S6. Solve the nominal performance index function set in step S5 to calculate a nominal optimal control sequence; construct a nominal hypothetical input sequence and a nominal hypothetical state sequence and transmit them to the following vehicle; calculate the nominal optimal state sequence using the nominal optimal control sequence and solve the auxiliary performance index function; apply the first element of the optimal control input of the solved auxiliary performance index function to the vehicle, completing full-condition control of the vehicle platoon;

[0240] Here are the steps:

[0241] S6.1. Perform initialization operations. The steps are as follows:

[0242] First, calculate offline the terminal elements The corresponding matrix of For terminal sets, is the terminal control law, is the terminal cost function; suppose there exists a matrix Make Stable, and The Jacobian matrix of the queue control model after the arrangement in step S4.4 is the state matrix and the input matrix respectively. Let where β i >1, is a symmetric positive semidefinite matrix and is The solution, and select the appropriate external interference and the Lipschitz coefficient corresponding to the state error and And the norm of the upper bound of external interference

[0243] When the speeds of all vehicles in the queue are equal and the acceleration inputs of the vehicles are all 0, the elements in the hypothetical input sequence of vehicle i and the hypothetical input sequence of vehicle i-1 are all inputs when the vehicles are in equilibrium. wji =F zji f r r wi, the corresponding assumed vehicle state and predicted vehicle state are calculated through the discrete vehicle model. The expression is as follows:

[0244]

[0245] Where, and are the nominal assumed state variables and nominal predicted state variables of vehicle i at step k at time 0, and are the nominal assumed state variables and nominal predicted state variables of the vehicle i-1 node at time 0, step k, respectively;

[0246] and The calculation process is as follows:

[0247]

[0248] Where, and are the nominal predicted state variables of vehicle i at time 0, step 0, step k, and step k+1, respectively. is the nominal hypothesis input of the kth step at time 0, is the nominal predicted state of the vehicle i control model at time 0, step k, is the nominal assumed state variable of vehicle i at step k at time 0, z i (0) is the measured value of the state variable of vehicle i node at the current moment;

[0249] S6.2: At any time t, solve the nominal optimization problem S5.1 of the control model for vehicle i to obtain the nominal optimal predictive control input sequence k=0,…,k p1 -1;

[0250] S6.3: Pass Calculate the nominal optimal state sequence at the current moment And the nominal optimal state sequence of the control model k=0,…,k p1 -1, the specific expression is as follows:

[0251]

[0252] Where, and are the nominal assumed state variables of vehicle i at step 0, step k and step k+1 at time t+1, is the nominal hypothesis input for the kth step at time t+1, is the nominal assumed state of the vehicle i control model at the kth step at time t+1, is the nominal assumed state variable of vehicle i at step k at time t+1, is the nominal optimal state variable of vehicle i node in the first step at time t;

[0253] S6.5: Apply the first control variable u of the auxiliary optimal predictive control input sequence obtained by solving the optimization problem on vehicle i i (0|t);

[0254] S6.6: Calculate the nominal hypothetical input sequence for the next step. Shift the nominal optimal control sequence at time t to the left, except for the first control input. Assume that the predicted terminal control input is the relationship between the terminal control law and the terminal state. Obtain the corresponding hypothetical output sequence, which is expressed as follows:

[0255]

[0256] Where, is the nominal hypothesis input for the kth step at time t+1, is the nominal optimal control input for the k+1th step at time t, is the nominal optimal state of the vehicle i control model at time t, is the terminal control law;

[0257] Accordingly, the vehicle state calculation formula is as follows:

[0258]

[0259] Where: and are the nominal assumed state variables of vehicle i at step 0, step k and step k+1 at time t+1, is the nominal hypothesis input for the kth step at time t+1, is the nominal assumed state of the vehicle i control model at the kth step at time t+1, is the nominal assumed state variable of vehicle i at step k at time t+1, is the nominal optimal state variable of vehicle i node in the first step at time t;

[0260] S6.7: Receive the nominal assumed vehicle state sequence of the preceding vehicle through vehicle-to-vehicle communication Construct a control model and Assume that the control sequence Send to the following car;

[0261] S6.8: Return to step S6.2 to implement rolling time domain control.

[0262] In order to verify the present invention, a simulation experiment was conducted. The masses of the following vehicles were set to 1100 kg, 1800 kg, and 1650 kg. The corresponding wheel radii were 0.31 m, 0.32 m, and 0.32 m, respectively. The horizontal distances from the front axle to the center of mass were 1.04 m, 1.35 m, and 1.4 m, respectively. The horizontal distances from the rear axle to the center of mass were 1.56 m, 1.55 m, and 1.65 m, respectively. The wheel moments of inertia were 0.6 kg m 2 、0.9kg﹒ m 2 、0.9kg﹒ m 2 The vehicle center of mass heights are 0.54m, 0.7m, and 0.53m respectively. The rest of the model parameters are the same, specifically: g = 9.81m / s2, fr = 0.02. The expected distance d when the vehicle is stationary sta = 10m, headway is h w = 0.5s, the discrete time is Δt = 0.001s, and the nominal prediction time domain and auxiliary prediction time domain of all vehicles are k p1 =k p2 = 10. The slip ratio is constrained to -0.1≤δ xj ≤0.1, vehicle input constraint is -1000Nm≤T wj ≤1000Nm. Except for the terminal parameters, the control weight coefficient matrix of the nominal optimization problem is the same for all vehicles, specifically: β=1.5. According to S6.1 and the corresponding weight coefficient matrix, the terminal element can be calculated, and the appropriate Lipschitz coefficient corresponding to the external interference and state error can be selected. and And the norm of the upper bound of external interference The weight coefficient matrices of the auxiliary optimization problems are the same, specifically: Q = diag(10,10,1,1), R = diag(0.001,0.001), P = diag(1,0.1), O = diag(10,10,1,1). Each following vehicle inputs an external disturbance with an amplitude of 0.2m / s2 and a frequency of 1rad / s. The upper bound of the pipeline is And the upper bound of the pipeline change rate The initial conditions of the vehicle are set as follows: x0 = 60 m, v0 = 20 m / s, x1 = 40 m, v1 = 20 m / s, x2 = 20 m, v2 = 20 m / s, x3 = 0 m, v3 = 20 m / s, μ = 0.85 for high-adhesion road surfaces, and μ = 0.3 for low-adhesion road surfaces.

[0263] Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9This is the simulation result of the queue control method under extreme working conditions based on pipeline distributed model predictive control using the above examples and parameters. Figure 4 and Figure 7 It can be seen that the distance between the fleets of the present invention is controlled within 1m on both high-adhesion and low-adhesion roads, indicating that the synchronization between the vehicles of the present invention is good; Figure 5 and Figure 8 It can be seen that the acceleration of the present invention is always within the safe range on high-adhesion and low-adhesion roads, verifying the validity of the tire force linearization assumption; Figure 6 and Figure 9 As can be seen, the longitudinal slip rate of the present invention ultimately approaches zero on both high- and low-adhesion surfaces, demonstrating the present invention's robustness under extreme operating conditions. The control method of the present invention maintains platoon stability and vehicle slip rates within the constraints, regardless of whether the vehicle is operating on high- or low-adhesion surfaces.

[0264] The above descriptions are only partial embodiments of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and modifications without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A vehicle platoon control method based on pipeline distributed model predictive control, characterized in that: The following steps are involved: S1. Based on longitudinal dynamics, a nodal vehicle model including nonlinear tire forces and wheel rotational dynamics is constructed by introducing the magic formula, normal force calculation, slip rate and rotational dynamics equations; S2, the vehicle nonlinear tire force is linearized, and the slip slope is estimated and the longitudinal stiffness of the wheel is calculated using the recursive least squares method; S3. Based on S1 and S2, a discrete model of a single node vehicle model is constructed; S4. Based on the discrete model constructed in S3, calculate the node vehicle state sequence and send the state sequence of the vehicle to the following vehicle and receive the state sequence of the leading vehicle to build a platoon control model. S5. Setting the nominal performance index function and the auxiliary performance index function of the platoon vehicles, and using the longitudinal wheel slip rate as a constraint; S6. Solve the nominal performance index function set in step S5 to calculate the nominal optimal control sequence; A nominal hypothetical input sequence and a nominal hypothetical state sequence are constructed and passed to the following vehicle. The nominal optimal state sequence is calculated through the nominal optimal control sequence and the auxiliary performance index function is solved. The first element of the optimal control input of the solved auxiliary performance index function is applied to the vehicle to complete the full working condition control of the vehicle queue.

2. The vehicle platoon control method based on pipeline distributed model predictive control according to claim 1, characterized in that: The steps for constructing a nodal vehicle model that includes nonlinear tire forces and wheel rotational dynamics based on longitudinal dynamics by introducing the magic formula, normal force calculation, slip rate, and rotational dynamics equations are as follows: S1.

1. Define the longitudinal dynamic equation of the vehicle after disturbance, as follows: Where, is the longitudinal acceleration of vehicle i; m i is the mass of vehicle i; F xfi (t) and F xri (t) are the longitudinal tire forces on the front and rear wheels of vehicle i; g is the acceleration due to gravity; f r is the rolling resistance coefficient; i (t) is the acceleration disturbance caused by external disturbance and modeling error; S1.

2. The longitudinal tire force of the vehicle is modeled based on the magic formula tire force model to reflect nonlinear tire forces. The expression is as follows: F xji (t)=μD xji (t)sin(C x arctan(B xji (t)Φ xji (t))); Φ xji (t)=(1-E xji (t))δ xji (t)+(E xji (t) / B xji (t))arctan(B xji (t)δ xji (t)); Where, j = f, r, when j is f, it is the front wheel, when j is r, it is the rear wheel; μ is the road adhesion coefficient; C x is the coefficient term; α1 to α8 are the first to eighth constant terms; e is the base of the natural logarithm; F zji (t) is the normal force of wheel j; δ xji (t) is the longitudinal slip rate of wheel j; S1.

3. Considering the effect of vehicle acceleration on tire loads, calculate the normal forces on the front and rear wheels using the following expressions: Where a i (t) is the longitudinal acceleration of vehicle i, let h c is the height of the vehicle's center of mass; l f and l r are the horizontal distances from the center of mass to the front and rear axles of the vehicle respectively; l is the wheelbase of the vehicle and l=l f +l r ; S1.

4. Calculate the longitudinal slip of wheel j to distinguish between acceleration and braking conditions. The expression is as follows: Where r wi is the tire radius of vehicle i; v i (t) is the vehicle speed; ω wji (t) is the rotational angular velocity of wheel j; S1.

5. Calculate the wheel angular velocity based on the rotational dynamics equation. The expression is as follows: Where, I w is the moment of inertia; is the derivative of the angular velocity of wheel j; T wji (t) is the torque applied to wheel j; F xji (t) is the longitudinal force of wheel j; S1.

6. Based on S1.4, the longitudinal slip derivative of wheel j during acceleration and deceleration can be obtained as follows: Where, is the derivative of the longitudinal slip rate of wheel j; S1.

7. Substitute S1.1 and S1.5 into S1.6 to eliminate the derivative term. The expression is as follows:

3. The vehicle platoon control method based on pipeline distributed model predictive control according to claim 1, characterized in that: The nonlinear tire force of the vehicle is linearized, and the slip slope is estimated and the longitudinal stiffness of the wheel is calculated using the recursive least squares method. The steps are as follows: S2.

1. On low-adhesion roads, the tire force of a vehicle is expressed as follows: F xji (t)=k xji (t)δ xji (t),j=f,r Where k xji (t) is the longitudinal stiffness of wheel j; let in, The coefficient used to describe the difference between the front tire stiffness and the rear tire stiffness when the vehicle is in all-wheel traction or braking conditions. Then the vehicle is rear-wheel drive or braked; S2.2 The relationship between tire longitudinal force and slip is expressed as follows: Where, F xi (t) is the sum of the longitudinal tire forces of the vehicle, F xi (t) = F xfi (t)+F xri (t); k ri (t) is the estimated slip slope; is the regression vector; S2.

3. Based on S2.2, the recursive least squares method is used to estimate the vehicle slip slope, which is expressed as follows: Where θ i (t) is the estimated slip slope, corresponding to θ in S2.2 i (t) = k ri Part (t); is the estimated regression vector, corresponding to S2.2 Part; y i (t) is the estimated longitudinal tire force of the vehicle, corresponding to F in S2.2 xi Part (t); S2.

4. Based on S2.3, calculate the estimated error using the estimated output. The estimated error is the difference between the current actual output and the estimated output predicted at the previous moment. The expression is as follows: Where, e fi (t) is the estimation error; θ i (t-1) is the estimated slip slope at the previous moment; S2.

5. Construct the gain vector and covariance matrix. The calculation method is as follows: Where K i (t) is the gain vector; P i (t) is the covariance matrix; P i (t-1) is the covariance matrix of the previous moment; λ1 is the forgetting factor, 0.9≤λ i ≤1; S2.

6. Update the estimated vehicle slip slope, expressed as: θ i (t)=θ i (t-1)+K i (t)e fi (t); S2.

7. Calculate the vehicle longitudinal stiffness based on the updated vehicle slip slope estimate using the following expression: k xri (t)=k ri (t)F zri (t)。 4. The vehicle platoon control method based on pipeline distributed model predictive control according to claim 1, characterized in that: According to S1 and S2, the discrete model of the single node vehicle model is constructed as follows: S3.

1. Based on removing the last item of S1.1, that is, removing the influence of acceleration interference caused by external disturbances and modeling errors, construct the nominal discretization model of the node vehicle in S1.5, S1.7, and S2.

1. The expression is as follows: Where, f i z is the gradient of the nominal state variable of the system at time t; Δt is the discrete time; is the nominal state variable of vehicle node i, where is the nominal position of vehicle i, is the nominal longitudinal velocity of vehicle i, and are the nominal longitudinal slip rates of the front and rear wheels of vehicle i, respectively; is the system nominal input, and are the nominal torques for the front and rear wheels, respectively; S3.

2. Based on S3.1, calculate the nominal state variable of vehicle node i. The expression is as follows: Where, and are the nominal positions of vehicle i at time t+1 and time t, respectively; and are the nominal longitudinal velocities of vehicle i at time t+1 and time t, respectively; and are the nominal longitudinal slip rates of wheel j at time t+1 and time t, respectively; is time t The gradient of change; is time t The gradient of change; S3.

3. Calculate the discretization of wheel speed. The expression is as follows: Where, and are the nominal rotational angular velocities of wheel j at time t+1 and time t, respectively; for The gradient of change at time t.

5. The vehicle platoon control method based on pipeline distributed model predictive control according to claim 1, characterized in that: The discrete model constructed according to S3 calculates the node vehicle state sequence and sends the state sequence of the vehicle to the following vehicle and receives the state sequence of the leading vehicle to construct a platoon control model. The steps are as follows: S4.

1. The vehicles in the queue adopt a timed distance formation strategy, and the expected distance d of vehicle i i (t) is expressed as follows: Where, d sta is the safe distance when the vehicle is stationary; h w is the headway; is the speed of vehicle i; S4.

2. Calculate the vehicle following distance error using the following expression: Where p i-1 (t) and p i (t) are the positions of vehicle i and vehicle i-1 respectively; is the speed of vehicle i during car-following; S4.

3. The motion state sequence of the preceding vehicle is obtained through vehicle-to-vehicle communication. The expression of the platoon control model is as follows: Where, and denote the first matrix and the second matrix respectively, is the nominal state variable of the queue control model; Nominal state variables of vehicle i-1 node; is the nominal state variable of vehicle node i; S4.

4. Based on S3.1, the vehicle state at the next moment needs to be predicted based on the vehicle state at the current moment and the control input. The platoon control model in S4.3 is organized and constraints are set. The expression is: Where, is the nominal state variable of the control model, where f i is a nonlinear function determined by the nodal vehicle dynamics model; The queue control model is constrained by state variables and control inputs, and is expressed as follows: Where, is the state constraint set; is the input constraint set.

6. The vehicle platoon control method based on pipeline distributed model predictive control according to claim 1, characterized in that: The steps for setting the nominal performance index function and the auxiliary performance index function of the platoon vehicles and taking the wheel longitudinal slip rate as a constraint are as follows: S5.

1. At time t, after constructing the local nominal optimal control problem expression for vehicle i and setting the cost function, construct the cost function of the local nominal optimal control problem expression for vehicle i; The optimal control problem is as follows: Where, The nominal predicted state sequence of the control model for vehicle i; The nominal forecast input sequence for the control model of vehicle i; is the nominal assumed state sequence of the control model for vehicle i-1; and They are the 0th and kth steps at time t respectively p1 -1 step vehicle i control model nominal prediction input, k p1 is the nominal forecast horizon; The expression to set the constraint is as follows: Where, and are the nominal predicted state and nominal predicted input of the control model of vehicle i at the kth step at time t, respectively; and are the nominal predicted states of the control model of vehicle i at time t, step k+1 and step 0 respectively; x i (t) is the measured value of the state variable of the control model at time t; is the terminal set; The cost function of the local nominal optimal control problem expression for vehicle i is as follows: Where, is the nominal assumed state of the control model of vehicle i-1 at time t, step k; is the nominal state weight matrix of the control model; Enter the weight matrix for nominal control; is the weight matrix of the following vehicle; is the terminal constraint matrix; S5.

2. At time t, after constructing the local auxiliary optimal control problem expression for vehicle i and setting constraints, construct a cost function for the local auxiliary optimal control problem expression for vehicle i; The local auxiliary optimal control problem of vehicle i is expressed as follows: Where, is the nominal optimal state sequence; x i The control model predicts the state sequence for vehicle i; u i Predict the input sequence for the control model of vehicle i; u i (0|t) and u i (k p2 -1|t) are the 0th and kth steps at time t respectively p2 -1 step vehicle i control model prediction input, k p2 Predicting the time domain for auxiliary control; The expression to set the constraint is as follows: x i (k+1|t)=f i (x i (k|t),u i (k|t)) s i (k+1|t)=s i (k|t)+λ i (k|t)Δt x i (k|t)∈X i ,u i (k|t)∈U i x i (k p2 |t)∈X fi Where x i (k+1|t) is the predicted state of the auxiliary controller at the k+1th step at time t; x i (k|t) is the predicted state at time t, step k; u i (k|t) is the predicted input of the auxiliary controller at time t, step k; s i (k+1|t) and s i (k|t) are the pipeline sizes of the k+1th step and the kth step at time t; λ i (k|t) is the pipeline change rate at step k at time t; and are the upper bound of the pipeline at the kth step at time t and the upper bound of the pipeline change rate; O i is the weight coefficient matrix describing the pipe shape; ν i (k|t) is the tightening constraint coefficient of the kth step at time t; in and are the Lipschitz coefficients corresponding to external interference and state error, is the norm of the upper bound of external interference; X i and U i are auxiliary controller state constraints and control input constraints respectively, X fi Auxiliary control terminal set; The cost function of the local auxiliary optimal control problem expression of vehicle i is as follows: Where, is the nominal optimal predicted state of the vehicle i control model at the kth step at time t, x i (k|t) and u i (k|t) are the predicted state and predicted input of the control model of vehicle i at the kth step at time t, S i (k|t) is the pipeline size and pipeline change rate at the kth step at time t, S i (k|t)=[s i (k|t),λ i (k|t)] T where s i (k|t) and λ i (k|t) are the pipeline size and pipeline change rate of the kth step at time t, Q i To control the auxiliary state weight matrix of the model, R i Input weight matrix for auxiliary control, P i is the pipeline weight matrix.

7. The vehicle platoon control method based on pipeline distributed model predictive control according to claim 1, characterized in that: The nominal performance index function set in step S5 is solved to calculate a nominal optimal control sequence; a nominal hypothetical input sequence and a nominal hypothetical state sequence are constructed and transmitted to the following vehicle; a nominal optimal state sequence is calculated using the nominal optimal control sequence and the auxiliary performance index function is solved; the first element of the optimal control input of the solved auxiliary performance index function is applied to the vehicle to complete the full-condition control of the vehicle platoon as follows: S6.

1. Perform initialization operations. The steps are as follows: First, calculate offline the terminal elements The corresponding matrix of For terminal sets, is the terminal control law, is the terminal cost function; suppose there exists a matrix Make Stable, and The Jacobian matrix of the queue control model after the arrangement in step S4.4 is the state matrix and the input matrix respectively. Let where β i >1, is a symmetric positive semidefinite matrix and is The solution, and select the appropriate external interference and the Lipschitz coefficient corresponding to the state error and And the norm of the upper bound of external interference When the speeds of all vehicles in the queue are equal and the acceleration inputs of the vehicles are all 0, the elements in the hypothetical input sequence of vehicle i and the hypothetical input sequence of vehicle i-1 are all inputs when the vehicles are in equilibrium. wji =F zji f r r wi , the corresponding assumed vehicle state and predicted vehicle state are calculated through the discrete vehicle model. The expression is as follows: Where, and are the nominal assumed state variables and nominal predicted state variables of vehicle i at step k at time 0, and are the nominal assumed state variables and nominal predicted state variables of the vehicle i-1 node at time 0, step k, respectively; and The calculation process is as follows: Where, and are the nominal predicted state variables of vehicle i at time 0, step 0, step k, and step k+1, respectively. is the nominal hypothesis input of the kth step at time 0, is the nominal predicted state of the vehicle i control model at time 0, step k, is the nominal assumed state variable of vehicle i at step k at time 0, z i (0) is the measured value of the state variable of vehicle i node at the current moment; S6.2: At any time t, solve the nominal optimization problem S5.1 of the control model for vehicle i to obtain the nominal optimal predictive control input sequence S6.3: Pass Calculate the nominal optimal state sequence at the current moment And the nominal optimal state sequence of the control model The specific expression is as follows: Where, and are the nominal assumed state variables of vehicle i at step 0, step k and step k+1 at time t+1, is the nominal hypothesis input for the kth step at time t+1, is the nominal assumed state of the vehicle i control model at the kth step at time t+1, is the nominal assumed state variable of vehicle i at step k at time t+1, is the nominal optimal state variable of vehicle i node in the first step at time t; S6.5: Apply the first control variable u of the auxiliary optimal predictive control input sequence obtained by solving the optimization problem on vehicle i i (0|t); S6.6: Calculate the nominal hypothetical input sequence for the next step. Shift the nominal optimal control sequence at time t to the left, except for the first control input. Assume that the predicted terminal control input is the relationship between the terminal control law and the terminal state. Obtain the corresponding hypothetical output sequence, which is expressed as follows: Where, is the nominal hypothesis input for the kth step at time t+1, is the nominal optimal control input for the k+1th step at time t, is the nominal optimal state of the vehicle i control model at time t, is the terminal control law; Accordingly, the vehicle state calculation formula is as follows: Where: and are the nominal assumed state variables of vehicle i at step 0, step k and step k+1 at time t+1, is the nominal hypothesis input for the kth step at time t+1, is the nominal assumed state of the vehicle i control model at the kth step at time t+1, is the nominal assumed state variable of vehicle i at step k at time t+1, is the nominal optimal state variable of vehicle i node in the first step at time t; S6.7: Receive the nominal assumed vehicle state sequence of the preceding vehicle through vehicle-to-vehicle communication Construct a control model and Assume that the control sequence Send to the following car; S6.8: Return to step S6.2 to implement rolling time domain control.

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