Hybrid vehicle platoon control method based on self-triggered pipeline model predictive control

Abstract

The application discloses a hybrid vehicle platoon control method based on a self-triggered pipeline model predictive control, which predicts a triggering time of future communication by designing a self-triggering mechanism, so as to reduce the sampling times of vehicle states, avoid continuous communication between intelligent agents, reduce the frequency of communication, reduce the calculation times of optimization problems, and shorten the online optimization time. By means of adaptive sampling interval control and communication network resource scheduling, conflict-free transmission is realized.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, specifically a hybrid vehicle platoon control method based on self-triggered Tube Model Predictive Control (Tube MPC). The research focuses on the communication redundancy problem in hybrid vehicle platoons, and designs a hybrid vehicle platoon control scheme based on self-triggered Tube MPC. By designing an optimization problem, the trigger interval time is directly included in the objective function, enabling the control input and trigger interval time to be optimized together. This significantly reduces the waste of system communication resources while ensuring control performance. Background Technology

[0002] With rapid economic development, traffic congestion, traffic safety, and traffic pollution have become increasingly prevalent, making vehicle platooning control a research hotspot. Vehicle platooning control ensures stable close-range following of vehicles through onboard sensors and vehicle-to-vehicle communication, thereby improving road efficiency and fuel economy. Existing research has confirmed that effective vehicle platooning control can improve traffic safety and reduce traffic energy consumption and pollution. Domestic and international research on vehicle platooning control primarily focuses on fully intelligent connected traffic environments, controlling autonomous vehicles (CAVs). However, real-world traffic environments are complex. Since the penetration rate of CAVs in traffic systems will remain unsaturated for a long time, the mixed distribution of manually driven and autonomous vehicles is an inevitable stage in real-world traffic environments. Furthermore, manually driven vehicles (HDVs) exhibit unpredictable uncontrollability and strong randomness. Vehicle platooning control methods designed for fully intelligent connected traffic environments cannot directly handle platoons containing HDVs, as the uncontrollability and strong randomness of HDVs can affect platooning safety. Therefore, vehicle platooning control methods for autonomous vehicles are not suitable for real-world traffic environments; thus, research into control methods for mixed vehicle platoons is necessary.

[0003] Model predictive control (MPC) is a commonly used method for implementing hybrid vehicle platoon control. This method excels at handling constrained multi-input multi-output (MIMO) systems, and its rolling time-domain prediction mechanism provides it with a degree of robustness. Since MPC is model-based control, the accuracy of the controlled system model directly affects the control performance of the MPC controller; therefore, model establishment is crucial. Existing research often involves designing MPC controllers to plan optimal trajectories for vehicle-to-everything (CAVs), thereby achieving coordinated control of the entire platoon. Vehicle-to-vehicle (V2V) communication and vehicle-to-infrastructure (V2I) communication are prerequisites for vehicle platoon control. Due to bandwidth limitations and channel congestion, improving information transmission efficiency becomes a critical aspect of problem-solving, making the online computational load of the controller particularly important. Under the premise of ensuring performance, the lower the system computational load, the less resource waste.

[0004] Existing research confirms that the TubeMPC control strategy can effectively address the model mismatch problem mentioned above. First, feedforward control is used to plan the optimal trajectory of the nominal system in the prediction time domain. Then, closed-loop feedback control constrains the actual states of all vehicles in the mixed platoon within the Tube positive invariant set, ultimately converging the system to its terminal state constraint set, thereby achieving robust cooperative control of the mixed vehicle platoon.

[0005] In recent years, non-periodic control for multi-agent systems has been broadly categorized into event-triggered control and self-triggered control. Event-triggered mechanisms require continuous communication between neighbors to exchange information and calculate the trigger time. Due to this unnecessary communication, the system suffers from a heavy communication burden. In contrast, self-triggered control strategies directly predict the next trigger time based on information collected at the current moment. It does not require acquiring neighbor information between two trigger times, avoiding periodic checks of the event trigger function, effectively reducing the number of controller updates, and conserving system communication and computational resources.

[0006] This research aims to reduce the communication frequency of hybrid vehicle platoons. It innovatively combines self-triggering with pipeline model predictive control (MMPC) to design a hybrid vehicle platoon control scheme based on self-triggering TubeMPC. The nominal system control input and trigger interval are used as decision variables. A self-triggering MPC optimization problem is designed, directly incorporating the trigger interval into the objective function. This allows for the joint optimization of the control input and the next trigger moment, achieving self-triggering control. The agent receives state estimation information and output estimation error from its neighbors at the current trigger moment to calculate the next trigger moment. To minimize communication between the system and the controller, the time interval from each sampling moment to the next sampling moment is calculated as part of the optimization problem solution. Between two trigger moments, neighbor information is not acquired; the system input before the next sampling moment is the control input of the previous sampling moment, effectively reducing the number of system communications and minimizing communication resource waste. To ensure that state and input constraints are satisfied under all possible disturbances, a Luneburger observer is designed to solve for the robust positive invariant sets of state estimation errors and control errors. This allows the hybrid vehicle platoon to overcome the negative effects of model mismatch and still guarantee the safety of platooning.

[0007] In summary, currently there is no pipeline model predictive control method that considers self-triggering mechanisms for mixed vehicle platoons. This reduces the computational update of the trigger sampling controller, lowers the system's communication frequency, alleviates the controller's computational burden, reduces communication resource waste, and has almost no performance loss compared to systems controlled by periodic sampling controllers. Summary of the Invention

[0008] The purpose of this invention is to provide a novel hybrid vehicle queuing control method. This method predicts the triggering time of future communication by designing a self-triggering mechanism, thereby reducing the number of vehicle state samples and avoiding continuous communication between agents. This reduces the communication frequency, decreases the number of optimization problem calculations, and thus shortens the online optimization time. Collision-free transmission is achieved through adaptive sampling interval control and communication network resource scheduling.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A vehicle queuing control method based on self-triggering Tube MPC model predictive control, characterized in that:

[0011] Includes the following steps

[0012] Step 1: Establish a mathematical model for the mixed vehicle queue

[0013] Step 1.1 Hybrid vehicle queue data representation

[0014] The hybrid vehicle platoon studied in this invention is randomly arranged, containing a total of m vehicles, consisting of l autonomous vehicles and m-1 manually driven vehicles. The CAVs (Autonomous Vehicles) can share vehicle dynamic information through V2V (Vehicle-to-Vehicle) and V2I (Vehicle-to-Infrastructure) methods, while the dynamic information of the HDVs (Autonomous Vehicles) can also be obtained through road testing equipment. Therefore, the dataset of the time-evolving hybrid vehicle platoon used in this paper can be represented as follows:

[0015]

[0016] Among them, v i and h i Let $\frac{i}{i}$ be the following speed and following distance of the $i$-th vehicle, respectively. The state of the mixed vehicle queue at time $k$ is defined as follows: Let T be the set of real numbers, and let T be the matrix transpose symbol. i，k =[h i，k v i，k ] T , i = 1, ..., m. h i，k v represents the distance between the (i-1)th car and the ith car at time k. i，k Let be the speed of the i-th vehicle. The control quantity of the mixed vehicle queue at time k is defined as... u i，k Let k represent the control input, i.e., acceleration, applied to the i-th autonomous vehicle at time k.

[0017] Step 1.2 Establish a discrete state-space model of the mixed vehicle queue

[0018] x k+1=Ax k +Bu k (1.2)

[0019] The control objective is to achieve a desired state for the entire hybrid vehicle platoon through control of CAVs, namely, a balanced state where vehicle speed and spacing are as expected. Considering modeling errors, an error term w is introduced. k Update the hybrid vehicle queue model as follows:

[0020] x k+1 =Ax k +Bu k +w k (1.3)

[0021] This invention establishes a system model based on Koopman operator theory. According to Koopman operator theory, the actual system state x k Mapped to a higher-dimensional space, represented as s k , improve state s k With actual state x k The relationship can be described as s k =Ψ(x k ), where Ψ(x) is the lifting function in Koopman operator theory. The resulting linear model of the mixed vehicle queue is:

[0022]

[0023] s k =Ψ(x k (1.5)

[0024] System matrix A and control matrix B can be obtained by solving an optimization problem. 1 represents the number of autonomous vehicles, and N represents the dimension of the elevated states. The mapping matrix C can be obtained using the least squares method. The calculation of parameters A, B, and C follows the Extended Dynamic Mode Decomposition (EDMD) algorithm, which is not the focus of the invention and will not be elaborated upon.

[0025] Step 1.3 Establish a hybrid vehicle queue incremental model

[0026] Since this invention designs the controller based on an incremental model, it is necessary to convert the physical model into an incremental model. In equilibrium, the vehicle's balance control quantity u... * =0. The total modeling error is denoted as . The linear incremental model of the hybrid vehicle queuing system with model error is as follows:

[0027]

[0028] Δs k =Ψ(Δx)k (1.7)

[0029] Where, Δs k =s k -s * ,Δu k =u k , Compact and containing the origin.

[0030] Step 2: Design a hybrid vehicle queue state estimation method based on Luneburger observers

[0031] Step 2.1: Construct the Luneburg state observer equations:

[0032] In actual queue operation, errors exist between the actual system state values ​​and the estimated state variables, resulting in a non-zero output error. A gain matrix L is designed to reduce the negative impact of accumulated errors through feedback correction, driving the estimated state variables to quickly converge to their actual values ​​and ensuring the observer's stability. A system state error is also introduced. In the observation model, this makes the output error approach zero more quickly, driving the observed state to approximate the actual system state. The Romberg state observer equations for the actual system are constructed as follows:

[0033]

[0034] Matrices A and B are approximations of the Koopman operator κ. From the decomposition, C is the mapping matrix that maps the system from the high-dimensional space back to the original spatial state. For the observer state, For observer output, It is the observer gain matrix.

[0035] Step 2.2: Construct the error equation for the state estimation of the mixed vehicle platoon

[0036] Define the state estimation error between the actual state values ​​and the estimated state variables of the system. for:

[0037]

[0038] By designing and selecting an appropriate feedback gain matrix L, the state estimation error can be brought close to zero, and the observer can eventually accurately observe the system state.

[0039] Step 3: Design feedback control for the self-triggering Tube controller

[0040] This section designs the feedback control component of a self-triggering Tube MPC controller for a hybrid vehicle platooning system. Tube MPC combines feedback control and feedforward MPC control to achieve better control performance. Feedback control dynamically reduces the deviation between the actual vehicle state and the nominal system state. First, the designed multi-objective optimization problem is solved using feedforward MPC control to plan the optimal trajectory for the nominal system. Then, a series of Tube pipes are constructed centered on the nominal system trajectory. Feedback control corrects the error between the actual and nominal states and guides the controlled vehicles to track the system within the Tube pipes, thus achieving robust control of the system even with model mismatch issues.

[0041] Step 3.1: Constructing an error system for the mixed vehicle queue

[0042] Considering the existence of the unknown disturbance ω, the actual state of the system is not identical to the nominal state. The actual boosted state Δs differs from the nominal boosted state. The deviation is σ. Define the actual state Δx and the nominal boosted state of the system. The deviation is K. As the control input to the error system, the error system for the mixed vehicle queue is obtained as follows:

[0043]

[0044] Step 3.2: Solve for the feedback control matrix K

[0045] After obtaining the error system of the mixed vehicle queue, in order to prevent the accumulation and propagation of errors, a closed-loop feedback auxiliary controller is designed for the error system of (2.1) to suppress the propagation of errors. The auxiliary feedback rate is:

[0046]

[0047] The feedback matrix K is obtained by establishing and solving the following discrete LQR linear quadratic regulator problem:

[0048]

[0049] Where Q and R are the weight matrices for the boost state and control input, respectively. A feedback controller is designed to dynamically adjust the deviation between the actual system and the nominal system, thereby improving the system's robustness.

[0050] The control power of the self-triggering Tube MPC algorithm consists of two parts. The control input of the actual system is:

[0051]

[0052] In the formula, and Let the nominal system control input and nominal escalation state of the mixed vehicle queue represent the respective steps. Step 3.3: Solve for the minimum RPI set.

[0053] The range of values ​​for the original state and control variables of the vehicle queuing system is narrowed, and the narrowed range is used as the nominal range of values ​​for the state and control variables. This ensures that the vehicle queuing system satisfies the original range of values ​​for the state and control variables even with approximation residuals, while maintaining the robustness of closed-loop control. Appropriate control inputs can be used to adjust the nominal system state of the hybrid vehicle queuing system. and the actual system state Δs k The error between them is always constrained within the robust positive invariant set of the error system.

[0054] Define the trigger time for each vehicle m as follows: The following is abbreviated as k i , The trigger interval is where This represents the maximum trigger interval. When k i ≤k<k i+1 That is, between two adjacent trigger times, because the system does not communicate, the control input... The values ​​remain unchanged. Therefore, the incremental model for the mixed vehicle queue is rewritten as:

[0055]

[0056] The Romberg state observer (2.1) is rewritten as follows:

[0057]

[0058] The control input is:

[0059]

[0060] The nominal system for the mixed vehicle queue is:

[0061]

[0062] The state estimation error equation is rewritten as:

[0063]

[0064] Define control error Its system equations are:

[0065]

[0066] The symbols are defined as follows:

[0067]

[0068]

[0069] in Then (1.12) and (1.13) can be rewritten as:

[0070]

[0071]

[0072] From v and From the definition, we can know Define the system (1.16) The RPI set is The RPI set of v in the system is Then there is in, Represents Minkowski addition, given a set For due to v and Bounded, an initial nominal state is determined by designing a self-triggering model predictive control algorithm. and a nominal control sequence and trigger interval Thus, the nominal system state sequence It asymptotically converges to zero, thus making the actual state Δx asymptotically bounded.

[0073] Due to mRPI set Since it is not easily obtained, an internal approximation method is used for approximation, and the formula is:

[0074]

[0075] Step 4: Design a self-triggered control strategy

[0076] Step 4.1: Design a self-triggered architecture for hybrid vehicle queuing

[0077] At each trigger moment, the sensor sends the current vehicle state information to the controller. The controller calculates the control input and the next trigger moment, and sends the control input to the actuator. The actuator controls the CAVs, and its control input remains unchanged until the next trigger moment. Communication between the sensor, actuator, and controller is only restored at the next trigger moment; communication is disconnected at other times.

[0078] The architecture of the self-triggered control system for hybrid vehicle platoons is as follows: Figure 1 As shown

[0079] Figure 1 Self-triggering control system architecture for hybrid vehicle platoons

[0080] Step 4.2: Design the trigger interval and objective function

[0081] The self-triggering Tube MPC controller at trigger time k i The open-loop multi-objective function is designed as follows:

[0082]

[0083] Where the trigger interval M∈N [1，p] It is a decision variable. These are design variables used to balance sampling costs and control costs. This reflects the sampling cost, which is used to weight the sampling cost with the performance cost of classical secondary control. and These are decision variables, for a given Choosing a larger τ forces M to be larger, resulting in a longer trigger interval and a significant reduction in the number of sampling triggers. This represents a trade-off between control performance and communication cost. By constructing a cost function, Q, R, and τ can be simulated and tuned to achieve the desired sampling behavior while maintaining the required control performance. It predicts the time domain. It is a stage cost. Let Q, R, and P be the terminal cost. Q, R, and P are all positive definite symmetric matrices. Q is the weight matrix of the original state of the nominal system of the hybrid vehicle queue, and R is the weight matrix of the control input. A symmetric positive definite matrix P is a solution to the following Lyapunov equation:

[0084]

[0085] Step 4.3: Obtain the input constraints for the mixed vehicle queue control.

[0086] The control input is obtained according to equation (3.7), and at time k i to k i+1 =k i +M is applied to the actuator. At trigger time k i+1 At this point, the system state is resampled and the control system is optimized. Afterwards, a size of... The system is controlled by a control signal with period p. The system samples at a faster rate during transients and at a slower rate when reaching steady state. This self-triggering mechanism's control sequence... follow Figure 2 The specific pattern shown is the control sequence. The following equality constraints must be satisfied:

[0087]

[0088] To meet safety control objectives, CAVs in a mixed vehicle platoon must satisfy relevant safety constraints, including state constraints such as following speed and following distance, as well as control constraints affected by the physical conditions of the CAVs themselves. The actual state, control variables, and constraints that the hybrid vehicle platoon must satisfy in its boost state are defined as follows:

[0089]

[0090] To ensure that the actual lifting state Δs and the control input Δu satisfy constraint (3.2), by and the control input of the actual system (3.7), the state of the nominal system and control applied to nominal systems Subject to the following tight constraints:

[0091]

[0092] In the formula Represents Pontryagin subtraction, given a set Where the terminal cost V f (·) and the terminal state constraint set S f The following assumptions are satisfied.

[0093] Assumption 4.1: Existence for and Make μ(k; x)∈S f , And V f (μ(k+1;x))-V f (μ(k;x))≤-l(μ(k+1;x),K f x), where

[0094] Step 5: Design the mixed vehicle queuing optimization problem

[0095] Step 5.1 Design the overall objective function

[0096] By directly incorporating the trigger interval M into the objective function, both the control input and the next trigger moment are optimized simultaneously, reducing the number of inter-system communications while maintaining system performance. The overall objective function is defined as follows:

[0097]

[0098] Step 5.2 Solving for the optimal sequence

[0099] Solving the optimal control problem Obtain the optimal trigger interval M * And optimal control sequence:

[0100]

[0101] and the corresponding optimal state sequence:

[0102]

[0103] the actual control quantity applied to systems (2.5) and (2.6) is:

[0104]

[0105] until the next triggering time k i+1 =k i +M * , the entire process is repeated.

[0106] Step 6: Calculate offline parameters

[0107] Step 6.1: Calculate the closed-loop feedback matrix K through (3.3);

[0108] Step 6.2: Calculate the RPI set through (3.15) and

[0109] Step 6.3: Calculate the tight set through (4.5) and

[0110] Step 6.4: Calculate the terminal weight matrix P through (4.2).

[0111] Step 7: Run online to solve the vehicle motion state

[0112] For the triggering moments k=k0, k1...k l ...k i

[0113] Step 7.1: Obtain the augmented state Δs through (1.7) k =Ψ(Δx k );

[0114] Step 7.2: Obtain the optimal solution through (5.1) M;

[0115] Step 7.3: Substitute the optimal solution into (3.4) to obtain the control input Δu k ;

[0116] Step 7.4: step<k+M, apply the control input Δu k to systems (3.5) and (3.6);

[0117] Step 7.5: Stop the calculation. Attached Figure Description

[0118] Figure 1 The architecture of a self-triggered control system for a mixed vehicle queue.

[0119] Figure 2 For when The predicted input and state sequence when p=4.

[0120] Figure 3 When τ = 0.2M = 10, the following speed, following distance, and following acceleration of the 5 vehicles under the self-triggered TubeMPC algorithm are as follows.

[0121] Figure 4 The triggering time distribution of 5 vehicles under the self-triggering TubeMPC algorithm when τ = 0.2M = 10.

[0122] Figure 5 The average trigger interval corresponding to different τ when M=10. Detailed Implementation

[0123] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0124] A hybrid vehicle queuing control method based on self-triggering model predictive control specifically includes:

[0125] Step 1: Modeling the hybrid vehicle queuing system;

[0126] Step 2: Design the Luneburg Observer;

[0127] Step 3: Design feedback control for the self-triggering Tube controller;

[0128] Step 4: Design a self-triggered control strategy;

[0129] Step 5: Design a mixed vehicle queuing optimization problem;

[0130] Step 6: Offline preparation;

[0131] Step 7: Online calculation;

[0132] This study designs a self-triggering TubeMPC controller and proposes a method to calculate the control signal at each sampling time and the optimal waiting time before the next sampling time, enabling centralized control of CAVs in the queue. The open-source Matlab toolboxes MPT3 and YALMIP are used, and a QP solver is employed to solve the linear quadratic programming problem. Results show that the controller is stable under mild assumptions. The designed self-triggering TubeMPC algorithm will be evaluated based on queue following performance and trigger time distribution. Simulation results show that compared to periodic sampling, this method reduces communication overhead with almost no performance loss.

[0133] The data from the offline calculations were stored in a memory. The specific steps for the online calculations are detailed in the invention description. The online calculations yielded simulation results. The total runtime was 40 seconds, or 400 simulation steps. Furthermore, the uncertainties for all vehicles were generated randomly using a uniform distribution, and the boundaries of the uncertainties were determined as follows: Figure 3 The spacing and speed responses of 5 vehicles under the self-triggered TubeMPC algorithm at τ=0.2 and M=10 are given, and the corresponding triggering times are shown in Figure 4.

[0134] like Figure 3 As shown, it can be seen that the states and control variables of all vehicles satisfy the constraints and can converge to a small range centered on the expected value, demonstrating strong robustness.

[0135] like Figure 4 As shown, the sampling time of the system is adaptively adjusted, and the trigger interval converges to p after reaching a steady state. This indicates that the self-triggering MPC algorithm proposed in this study can expand the sampling time interval to reduce the number of communications, further demonstrating that the self-triggering TubeMPC algorithm proposed in this study is feasible.

[0136] As mentioned above, The choice of τ, used to balance sampling and control costs, affects the trigger interval. This method chooses a fixed p value of 10 and calculates the average trigger interval before reaching steady state by varying the τ value. Figure 5 As shown, the average trigger interval monotonically increases with τ, indicating that the proposed self-triggering TubeMPC scheme can save more communication resources and has a lower sampling frequency. When τ is large, the number of communications decreases but the control performance deteriorates; when τ is small, the control performance is better but the number of communications increases. Therefore, choosing an appropriate value of τ is important.

Claims

1. A hybrid vehicle queuing control method based on self-triggering pipeline model predictive control, characterized in that: Includes the following steps: Step 1: Establish a mathematical model for the mixed vehicle queue; Step 1.1 Representation of hybrid vehicle queue data; The hybrid vehicle queue is randomly arranged and contains a total of m vehicles, consisting of l autonomous vehicles and ml manually driven vehicles. The dataset representing the hybrid vehicle queue as it evolves over time is shown below. D= (1.1) in, and Let $\frac{i}{i}$ be the following speed and following distance of the $i$-th vehicle, respectively; the state of the mixed vehicle queue at time $k$ is defined as... = , For the set of real numbers, This is the matrix transpose symbol; ,i=1,…,m; This represents the distance between the (i-1)th car and the ith car at time k. Let be the speed of the i-th vehicle; the control quantity of the mixed vehicle platoon at time k is defined as... , This represents the control input, i.e., acceleration, applied to the i-th autonomous vehicle at time k. Step 1.2 Establish a discrete state-space model of the mixed vehicle queue; (1.2) The control objective is to achieve the desired state of the entire hybrid vehicle platoon through the control of CAVs, i.e., the equilibrium state where vehicle speed and spacing are as expected; considering modeling errors, an error term is introduced. Update the hybrid vehicle queue model as follows: (1.3) A system model is established based on Koopman operator theory. According to Koopman operator theory, the actual system state... Mapped to a higher-dimensional space, represented as Improve status Compared with the actual state The relationship is described as ,in Let the lifting function be defined in Koopman operator theory, thus yielding the linear model of the mixed vehicle queue as follows: (1.4) (1.5) System Matrix Control matrix This is obtained by solving the optimization problem. Let l represent the number of autonomous vehicles, and N represent the dimension of the lifted states; the mapping matrix C is obtained using the least squares method. The calculation of parameters A, B, and C follows the extended dynamic mode decomposition algorithm; Step 1.3 Establish an incremental model for the mixed vehicle queue; The controller is designed based on an incremental model, transforming the physical model into an incremental model. In the equilibrium state, the vehicle's balance control quantity... =0; the total modeling error is denoted as . The linear incremental model of the hybrid vehicle queuing system with model error is as follows: (1.6) (1.7) in, = , , Compact and containing the origin; Step 2: Design a hybrid vehicle queue state estimation method based on Luneburger observers; Step 2.1: Construct the Luneburg state observer equations: Introducing system state error In the observation model, this makes the output error approach zero more quickly, driving the observed state to approximate the actual system state. The Romberg state observer equations for the actual system are constructed as follows: （2.1） Matrices A and B are defined by the Koopman operator. Approximate matrix From the decomposition, C is the mapping matrix that maps the system from the high-dimensional space back to the original spatial state. For the observer state, For observer output, It is the observer gain matrix; Step 2.2: Construct the error equation for the state estimation of the mixed vehicle platoon; Define the state estimation error between the actual state values ​​and the estimated state variables of the system. for: （2.2） By designing and selecting an appropriate feedback gain matrix L, the state estimation error can be brought close to zero, and the observer can eventually accurately observe the system state. Step 3: Design feedback control for the self-triggering Tube controller; The design incorporates the feedback control section of a self-triggering Tube MPC controller. Tube MPC combines feedback control and feedforward MPC control to achieve better control performance. Feedback control dynamically reduces the deviation between the vehicle's actual state and the nominal system state. Feedforward MPC control solves the designed multi-objective optimization problem, planning the optimal trajectory for the nominal system. A Tube pipeline is then constructed centered on the nominal system trajectory. Feedback control corrects the error between the actual and nominal states and guides the controlled vehicle through the Tube pipeline for tracking control, achieving robust control of the system even with model mismatch issues. Step 3.1: Construct an error system for the mixed vehicle queue; Actual improvement status With nominal promotion status The deviation is , Define the actual state of the system. With nominal promotion status The deviation is , , As the control input to the error system, the error system for the mixed vehicle queue is obtained as follows: （3.1） Step 3.2: Solve for the feedback control matrix K; After obtaining the error system of the mixed vehicle queue, a closed-loop feedback auxiliary controller is designed for the error system of equation (2.1) to suppress the propagation of error. The auxiliary feedback rate is: （3.2） The feedback matrix is ​​obtained by establishing and solving the following discrete LQR linear quadratic regulator problem. : （3.3） Where Q and R are the weight matrices for the boost state and control input, respectively; The control power of the self-triggering Tube MPC algorithm consists of two parts. The control input of the actual system is: （3.4） In the formula, and The nominal system control inputs and nominal lift states, respectively, represent the mixed vehicle platoon. Step 3.3: Solve for the minimum RPI set; The range of values ​​for the original state and control variables of the vehicle queuing system is narrowed, and the narrowed range is used as the nominal range of values ​​for the state and control variables of the system. This ensures that the vehicle queuing system satisfies the original range of values ​​for the state and control variables even with approximation residuals, while maintaining closed-loop control robustness. The nominal system state of the mixed vehicle queuing is then used as the control input. and actual system state The error between them is always constrained within the robust positive invariant set of the error system; Define the trigger time for each vehicle m as follows: , abbreviated as The trigger interval is where The maximum trigger interval; when That is, between two adjacent trigger times, because the system does not communicate, the control input... If the values ​​remain unchanged, then the incremental model of the mixed vehicle queue can be rewritten as follows: （3.5） The Luneburg state observer formula (2.1) is rewritten as: （3.6） The control input is: （3.7） The nominal system for the mixed vehicle queue is: （3.8） The state estimation error equation is rewritten as: （3.9） Define control error Its system equations are: （3.10） The symbols are defined as follows: （3.11） （3.12） in Then formulas (3.9) and (3.10) can be rewritten as follows: （3.13） （3.14） from and Definition, ;definition The RPI set is , The RPI set is Then there is ;in, Represents Minkowski addition, given a set ;because and Bounded, an initial nominal state is determined by designing a self-triggering model predictive control algorithm. and a nominal control sequence and trigger interval , making the nominal system state sequence Asymptotically converges to zero, actual state asymptotically bounded; mRPI set The approximation is performed using the inner approximation method, and the formula is as follows: （3.15） Step 4: Design a self-triggered control strategy; Step 4.1: Design a self-triggered architecture for hybrid vehicle queuing; At each trigger moment, the sensor sends the current vehicle status information to the controller. The controller calculates the control quantity and the next trigger moment, and sends the control input to the actuator. The actuator controls the CAVs, and its control quantity remains unchanged until the next trigger moment. Communication between the sensor, actuator, and controller is only restored at the next trigger moment, and communication is disconnected at other times. Step 4.2: Design the trigger interval and objective function; The self-triggering Tube MPC controller at the trigger time The open-loop multi-objective function is designed as follows: （4.1） Trigger interval It is a decision variable. These are design variables used to balance sampling costs and control costs; It reflects the sampling cost and is used to weight the sampling cost with the performance cost of classical secondary control. and These are decision variables; by constructing a cost function... , and Perform simulation optimization; It predicts the time domain. ; It is a stage cost. For terminal costs; , and Both are positive definite symmetric matrices; Q is the weight matrix of the original state of the nominal system of the hybrid vehicle queuing, and R is the weight matrix of the control input. The symmetric positive definite matrix P is a solution to the following Lyapunov equation: （4.2） Step 4.3: Obtain the input constraints for the mixed vehicle queue control; The control input is obtained according to formula (3.7), and at time... arrive Applied to the actuator; at the triggering time At that time, resample and optimize; use a size of The period is The control signal is used to control the system; the control sequence of the self-triggering mechanism. That is, control sequence The following equality constraints must be satisfied: （4.3） To meet safety control objectives, CAVs in a mixed vehicle platoon must satisfy relevant safety constraints, including following speed and following distance constraints, as well as control constraints affected by the physical conditions of the CAVs themselves. The constraints that the actual state, control variables, and lifting state of the mixed vehicle platoon must satisfy are defined as follows: （4.4） To ensure the actual improvement status and control input Satisfying constraint formula (4.4), by And the control input formula (3.7) of the actual system, the state of the nominal system and control applied to nominal systems Subject to the following tight constraints: （4.5） In the formula Represents Pontryagin subtraction, given a set Among them, terminal cost and terminal state constraint set The following assumptions are satisfied; Assumption: Existence ,for and , making , and ,in , ; Step 5: Design a mixed vehicle queuing optimization problem; Step 5.1 Design the overall objective function; The trigger interval M is directly included in the objective function, optimizing both the control input and the next trigger moment simultaneously, thereby reducing the number of inter-system communications while maintaining system performance; the overall objective function is defined as: (5.1) Step 5.2 Solve for the optimal sequence; Solving the optimal control problem Obtain the optimal trigger interval And optimal control sequence: （5.2） And the corresponding optimal state sequence: （5.3） The actual control quantities applied to formulas (3.5) and (3.6) are: （5.4） Until the next trigger time The entire process is repeated. Step 6: Calculate offline parameters; Step 6.1: Calculate the closed-loop feedback matrix using formula (3.3). ; Step 6.2: Calculate the RPI set using formula (3.15) and ; Step 6.3: Calculate the compact set using formula (4.5) and ; Step 6.4: Calculate the terminal weight matrix P using formula (4.2); Step 7: Solve the vehicle's motion state online; For triggering time ; Step 7.1: Obtain the boosted state using formula (1.7) ; Step 7.2: Obtain the optimal solution using formula (5.1) , , ; Step 7.3: Substitute the optimal solution into formula (3.4) to obtain the control input. ; Step 7.4: Control input Apply to formulas (3.5) and (3.6); Step 7.5: Stop the calculation.

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