Model-free adaptive control method for multi-intelligent heavy truck platoon, electronic device and storage medium

Abstract

The application provides a model-free adaptive control method for multi-intelligent heavy truck formation, an electronic device and a storage medium, and specifically comprises the following steps: analyzing the motion process of the heavy truck to obtain a nonlinear system; dynamically linearizing the nonlinear system, designing a TD-cMFAC controller based on time delay output prediction and input-output constraint processing; and controlling the heavy truck formation by using the TD-cMFAC controller. The technical scheme of the application overcomes the problem in the prior art that there is still a lack of efficient and reliable solutions for simultaneously processing unknown nonlinearities, unknown time delays, multi-agent collaboration and input-output constraints.

Description

Technical Field

[0001] This invention relates to the field of vehicle platooning control, specifically to a model-free adaptive control method, electronic device, and storage medium for multi-intelligent heavy truck platooning. Background Technology

[0002] Longitudinal multi-vehicle cooperative platoon control is a core technology in the field of intelligent connected vehicles. By platooning vehicles, air resistance can be significantly reduced, thereby lowering overall fleet fuel consumption and emissions and improving road traffic efficiency. However, achieving stable and safe truck platoon control faces many challenges: the dynamic model of heavy trucks has strong nonlinearity and time-varying parameters; communication between vehicles and the response of actuators have unknown and time-varying time delays; in addition, key parameters such as truck acceleration, speed, and spacing must be subject to strict physical constraints to prevent unrealistic or dangerous control commands.

[0003] Traditional model-based control methods, such as model predictive control and PID control, heavily rely on accurate mathematical models of the controlled object. For complex systems like multi-truck platoons, establishing accurate mathematical models is extremely difficult, and model mismatch, unknown time delays, and unmodeled dynamics can significantly degrade the performance of traditional controllers, even leading to system instability. While data-driven control methods offer new insights, existing solutions still lack efficient and reliable solutions for simultaneously handling the complex problems of unknown nonlinearities, unknown time delays, multi-agent cooperation, and input-output constraints.

[0004] Therefore, there is a need for a model-free adaptive control method, electronic device, and storage medium for multi-intelligent heavy truck platoons that does not rely on an exact mathematical model, can adaptively compensate for unknown time delays and nonlinearities, and can strictly guarantee system safety constraints. Summary of the Invention

[0005] The main objective of this invention is to provide a model-free adaptive control method, electronic device, and storage medium for multi-intelligent heavy truck platooning, in order to solve the problem that existing technologies still lack efficient and reliable solutions for the comprehensive problem of simultaneously handling unknown nonlinearity, unknown time delay, multi-agent cooperation, and input-output constraints.

[0006] To achieve the above objectives, this invention provides a model-free adaptive control method for multi-intelligent heavy truck platooning, specifically including the following steps: S1, perform motion analysis on the heavy truck to obtain a nonlinear system; S2, Dynamic linearization of nonlinear systems, and design of TD-cMFAC controller based on time delay output prediction and input-output constraint processing; S3 uses the TD-cMFAC controller to control the heavy truck platoon.

[0007] Furthermore, the vertical speed control dynamic system of the heavy truck in step S1 is a discrete-time nonlinear system: (1); in, Indicates the first The distance traveled by the heavy truck Indicates the first The acceleration of a heavy truck, Indicates time, Represents the time lag of a nonlinear system. Represents an unknown nonlinear function. and Let these represent the unknown input order and output order of the nonlinear system, respectively. This refers to the number of heavy trucks in the vehicle platoon.

[0008] Furthermore, step S2 specifically includes the following steps: S2.1, Discrete-time nonlinear systems (1) satisfy the generalized Lipschitz condition, that is, for any time... ,have: (2); Where, vector By sliding time window It consists of all the control inputs inside. A positive constant for the linearization length constant LLC. It is a positive number. The change in acceleration This represents the change in distance. S2.2, Discrete-time nonlinear system (1) has a time-varying vector called pseudo-gradient PG. This transforms the discrete-time nonlinear system (1) into a partially formatted dynamic linearized PFDL data model, as follows: (3); in, ; ,and It is a positive number; For signal, for The transpose of, and at any time There are boundaries.

[0009] Furthermore, step S2 also includes the following steps: S2.3, introducing the Smith estimation method, the dynamic linearization model is further transformed into: (4); in, It is a differential signal.

[0010] Furthermore, step S2 also includes the following steps: S2.4 uses graph theory to represent the communication and data transmission processes between vehicles, followers, and leaders: (5); (6); in, Indicates heavy truck , The communication status between them Indicates heavy truck The communication status between the facilitator and the guide; S2.5, considering the deviations between individual vehicles The definition is as follows: (7); in, It is the expected trajectory. It is a heavy truck The actual output.

[0011] Furthermore, step S2 also includes the following steps: S2.6, consider the following control input cost function : (8); in, As a weighting factor, The desired distance; To concisely express the subsequent formulas, the following definitions are given: (9); S2.7, Substituting formula (4) into formula (9) yields: (10); in, and They represent loaded vehicles respectively. and A set of.

[0012] The control inputs satisfy the inherent physical constraints of the loaded vehicle platooning system: (11); in, , These represent the lower and upper limits of allowed system input, respectively.

[0013] Furthermore, step S2 also includes the following steps: S2.8, the constraint (11) is integrated into the original cost function (8) using a quadratic penalty function to obtain the augmented output cost function. : (12); in, As a penalty factor, Let be a symmetric quadratic penalty function, defined as follows: (13); in, This is a function to find the maximum value. S2.9 Substituting formula (10) into the augmented output cost function (12) and setting the derivative to zero, the constraint control law can be obtained, which is the final constraint TD-cMFAC control law. Represented as: (14); in, Step size factor For the pseudo-partial derivative of the first heavy truck in the formation, for The estimated value, To control the input linearization length function, The constraint gradient term for the derivative of the penalty function: (15).

[0014] Furthermore, step S2 also includes the following steps: S2.10, Establish the criterion function Estimating the pseudo gradient PG: (16); in, The square of the norm; Selecting the optimal condition And using the matrix inverse lemma, the following results are obtained: (17); in, for The estimated value; As a weighting factor, Step size factor; S2.11, using the reset algorithm to perform pseudo gradient estimation for heavy truck platooning: (18); in, For positive integers, yes The first element, yes initial value, It is a symbolic function; S2.12, in order to obtain The delay output prediction TD is used, and the TD design is as follows: (19); in, for The estimated value, for The estimated value, It is the discrete sampling step size. These are tracking parameters. These are filter parameters. This is the fastest control synthesis function; S2.13, when obtained After obtaining the estimated value of PG, the control law (14) is rewritten in the following form: (20); (twenty one); in, Representing the The heavy truck receives the differential signal from TD. Representing the The heavy truck receives the differential signal from TD.

[0015] The present invention also provides an electronic device, which includes a processor and a memory communicatively connected to the processor; the memory stores instructions that are executed by the processor, which in turn execute a model-free adaptive control method for multi-intelligent heavy truck platooning.

[0016] The present invention also provides a storage medium, which is a computer-readable storage medium, and stores a computer program on the storage medium. When the computer program is executed by a processor, it implements a model-free adaptive control method for multi-intelligent heavy truck platooning.

[0017] The present invention has the following beneficial effects: This invention provides a highly efficient and robust longitudinal control scheme for heavy-duty truck platooning cooperation by employing a model-free adaptive control algorithm and considering practical application requirements, offering technical support for the application of unmanned heavy-duty truck platooning and freight transportation. This invention eliminates the need for establishing precise dynamic models of heavy-duty trucks, utilizing only the system's input and output data. It transforms the nonlinear time-delay system into a data model through dynamic linearization technology, incorporates a tracking differentiator for signal preprocessing, and designs a model-free adaptive controller with a penalty function optimization constraint mechanism. This method can estimate and compensate for unknown time delays and nonlinear dynamics in the system online, while ensuring that all control inputs and system outputs (such as acceleration and vehicle spacing) meet preset safety constraints, thereby achieving stable, efficient, and safe control for longitudinal platooning cooperation. The TD-cMFAC scheme proposed in this invention has superior performance, mainly based on the following two points: 1) Compared with the GWO-PID controller, the TD-cMFAC controller can comprehensively consider time delay and system constraints, effectively suppressing system oscillations and instability; 2) Compared with the IMFAC-TD controller that uses compact form dynamic linearization (CFDL) technology, this scheme captures the dynamic changes of historical data through partial form dynamic linearization technology, significantly improving the formation control accuracy. Attached Figure Description

[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 A flowchart of a model-free adaptive control method for multi-intelligent heavy truck platooning according to the present invention is shown.

[0019] Figure 2 A diagram of the communication topology for heavy truck platoons is shown.

[0020] Figure 3 A block diagram of the TD-cMFAC system is shown.

[0021] Figure 4 A comparison chart of heavy truck platooning speed curves under different control methods is shown.

[0022] Figure 5 A comparison chart of heavy truck platoon displacement curves under different control methods is shown.

[0023] Figure 6 A comparison chart of the platooning distance curves for heavy trucks under different control methods is shown. Detailed Implementation

[0024] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Example 1 like Figure 1 The model-free adaptive control method for multi-intelligent heavy truck platooning shown includes the following steps: S1, perform motion analysis on the heavy truck to obtain a nonlinear system; S2, Dynamic linearization of nonlinear systems, and design of TD-cMFAC controller based on time delay output prediction and input-output constraint processing; S3 uses the TD-cMFAC controller to control the heavy truck platoon.

[0026] Specifically, in the platooning control of heavy trucks, the input is the real-time acceleration of each truck, and the output is the travel distance of the heavy trucks. Since the acceleration of heavy trucks is not constant, there are many uncontrollable factors in the actual control process, so the relationship between them is actually nonlinear.

[0027] In step S1, the vertical speed control dynamic system of the heavy truck is a discrete-time nonlinear system. (1); in, Indicates the first The distance traveled by the heavy truck Indicates the first The acceleration of a heavy truck, Indicates time, Represents the time lag of a nonlinear system. Represents an unknown nonlinear function. and Let these represent the unknown input order and output order of the nonlinear system, respectively. This refers to the number of heavy trucks in the vehicle platoon.

[0028] In the longitudinal collaborative control of multiple truck platoons, such as Figure 2 As shown, all vehicles can rely on the technological advantages of inter-vehicle communication to obtain the motion status and changing trends of the following vehicle and the leader vehicle 0, and at the same time transmit their own motion status information (speed and acceleration) to other vehicles in real time, control the distance between vehicles, and improve driving stability.

[0029] Specifically, step S2 includes the following steps: S2.1 For the above system (1), before performing dynamic linearization modeling, the following assumptions are made: the discrete-time nonlinear system (1) satisfies the generalized Lipschitz condition, that is, for any time... ,have: (2); Where, vector By sliding time window It consists of all the control inputs inside. A positive constant for the linearization length constant LLC. It is a positive number. The change in acceleration This represents the change in distance. Except for finite time points, system control input signals partial derivatives All are continuous; S2.2, Discrete-time nonlinear system (1) has a time-varying vector called pseudo-gradient PG. This transforms the discrete-time nonlinear system (1) into a partially formatted dynamic linearized PFDL data model, as follows: (3); in, ; ,and It is a positive number; For signal, for The transpose of, and at any time There are boundaries; when When the value is not large, It can be regarded as a slowly time-varying parameter.

[0030] Specifically, step S2 also includes the following steps: S2.3, the hysteresis characteristics of the discrete-time nonlinear system described above cannot be directly applied to the controller. To address this issue, the Smith estimation method is introduced, and the control system structure is as follows: Figure 3 As shown, the transfer function of the controlled object is , This represents random perturbations in the system.

[0031] For slowly time-varying system parameters and structures, φs + 1 can be used instead of φs + 1. This completes the Smith estimation function. Furthermore, the MFAC controller has a strong ability to suppress external disturbances and changes in system parameters. Therefore, the dynamic linearization model can be further transformed into: (4); in, It is a differential signal.

[0032] In reality, latency is not arbitrarily large; it is bounded and can be defined as... .in, , These represent the minimum and maximum values ​​of the time delay, respectively. Similarly, the time delay may also be time-varying. This invention considers the worst-case scenario. Because the time delay has certain limits, i.e. .

[0033] Specifically, step S2 also includes the following steps: S2.4 In a vehicle queuing system, vehicles can exchange information. Graph theory is used to represent the communication and data transmission processes between vehicles, and between followers and leaders: (5); (6); in, Indicates heavy truck , The communication status between them Indicates heavy truck The communication status between the facilitator and the guide; S2.5, considering the deviations between individual vehicles The definition is as follows: (7); in, It is the expected trajectory. It is a heavy truck The actual output, the ultimate control objective is to enable all agents to achieve formation control based on the expected deviations of the navigator and other followers, according to the information of the local distribution.

[0034] Specifically, step S2 also includes the following steps: S2.6, consider the following control input cost function : (8); in, As a weighting factor, The desired distance; To concisely express the subsequent formulas, the following definitions are given: (9); S2.7, Substituting formula (4) into formula (9) yields: (10); in, and They represent loaded vehicles respectively. and A set of.

[0035] The control inputs satisfy the inherent physical constraints of the loaded vehicle platooning system: (11); in, , These represent the lower and upper limits of allowed system input, respectively.

[0036] Specifically, step S2 also includes the following steps: S2.8 To proactively address these constraints rather than employing simple post-computation pruning, this invention reformulates the controller design as a constrained optimization problem. Specifically, a quadratic penalty function is used to integrate the constraints (11) into the original cost function (8), resulting in the augmented output cost function. : (12); in, As a penalty factor, Let be a symmetric quadratic penalty function, defined as follows: (13); in, This is a function to find the maximum value. These penalty terms remain zero when the variable is within its boundary range, but increase quadratically when the constraint is violated, thus guiding the optimal solution away from the constraint boundary. The quadratic penalty function is chosen because of its smooth differentiability, which is compatible with the pseudo-gradient estimation framework of MFAC, and it has good numerical stability, avoiding control law oscillations caused by non-smooth penalty functions.

[0037] S2.9, Substituting formula (10) into the augmented output cost function (12) and setting the derivative to zero, we obtain the constraint control law. The derivative of the penalty term introduces an additional gradient component. The final constraint TD-cMFAC control law. Represented as: (14); in, Step size factor For the pseudo-partial derivative of the first heavy truck in the formation, for The estimated value, To control the input linearization length function, The constraint gradient term for the derivative of the penalty function: (15).

[0038] The constraint control law (14) proposed in this invention has a clear structure. The first two terms are the same as the unconstrained MFAC law, aiming to achieve tracking and consensus; the third term is a constraint correction term. This term actively adjusts when the control input approaches or violates the boundary. For example, when approaching the boundary, the correction term subtracts a positive value from the control update, thereby actively reducing the input to prevent constraint violation. The penalty factor determines the aggressiveness of this correction action. This mechanism ensures smooth, forward-looking constraint processing, which is superior to simple clipping methods.

[0039] Specifically, step S2 also includes the following steps: S2.10, to implement the control law (15), PG needs to be known; however, since PG is a time-varying vector, its true value is difficult to obtain. Establish the criterion function. Estimating the pseudo gradient PG: (16); in, The square of the norm; Selecting the optimal condition And using the matrix inverse lemma, the following results are obtained: (17); in, for The estimated value; As a weighting factor, Step size factor; S2.11 utilizes a reset algorithm to perform pseudo-gradient estimation on heavy truck platoons, thereby improving their ability to track time-varying parameters: (18); in, For positive integers, yes The first element, yes initial value, It is a symbolic function; S2.12, In practice, differential signals This method may not be able to handle the data directly, and it can lead to inaccurate measurements if subjected to external interference. In such cases, alternative strategies are needed for measurement. In order to obtain The time-delay output prediction (TD) is a dynamic system. TD generates two signals: one tracks the input signal. of The other is differential signal The design of TD is as follows: (19); in, for The estimated value, for The estimated value, It is the discrete sampling step size. These are tracking parameters. These are filter parameters. This is the fastest control synthesis function; S2.13, when obtained After obtaining the estimated value of PG, the control law (14) is rewritten in the following form: (20); (twenty one); in, Representing the The heavy truck receives the differential signal from TD. Representing the The heavy truck receives the differential signal from TD.

[0040] This invention uses the Auman Starwing LNG-powered BJ4259L6DLL-22 truck from Traffic Control Technology Co., Ltd. as the heavy-duty truck for the experiment. The developed heavy-duty truck autonomous driving platform is equipped with several key sensors, including millimeter-wave radar, a 2-megapixel camera, a Walsin combined antenna, a mesh module, a digital I / O controller, an Orin host, an inertial navigation system, and an onboard Ethernet converter, for collecting vehicle motion data. This motion information is transmitted via bus to the NVIDIA Jetson AGX Orin computing platform, which uses C++ programming based on the Ubuntu system to implement the controller functions. The steering commands calculated by the controller are then transmitted to the drive-by-wire chassis system to achieve platooning control of the heavy-duty trucks. In addition, this embodiment also uses two other control methods for comparison: PID control using the Grey Wolf Optimization (GWO) algorithm and IMFAC-TD.

[0041] The GWO-PID input can be mathematically expressed as follows: ; in, It is the proportional coefficient and the integral coefficient. and differential coefficients Determined using the Grey Wolf optimization algorithm.

[0042] The IMFAC-TD input can be mathematically expressed as follows: ; in, and These are parameters of the IMFAC-TD controller, and This represents the pseudo-partial derivative obtained by the estimation algorithm.

[0043] Table 1 shows the basic dynamic parameters of the heavy-duty truck. In this test, the heavy-duty truck operated linearly with time-varying longitudinal speeds within the range of [0, 80] km / h.

[0044] Table 1 Vehicle dynamic parameters The simulated road conditions consisted of a 5-kilometer straight road segment. Furthermore, Table 2 shows the parameters of the TD-cMFAC control scheme and the parameters of two other controllers used for comparison.

[0045] Table 2 Controller Parameters Three heavy-duty trucks were selected as simulation test subjects: Heavy-duty Truck 1, Heavy-duty Truck 2, and Heavy-duty Truck 3. The driving time for each truck was set to 100 seconds. Considering the high-speed driving environment, the reference speed curves for the heavy-duty trucks were constructed as follows: ; To verify the robustness of the TD-cMFAC control scheme, uncertainty was introduced into the system by setting a penalty function. A constraint was imposed on the heavy trucks: the truck speed must not exceed 70 km / h. Heavy truck 1 acts as the guide truck, heavy truck 2 receives information from heavy truck 1, and heavy truck 3 receives information from heavy truck 2. Simulation results are as follows: Figure 4-6 As shown.

[0046] Figure 4-6 The study demonstrates that while TD-cMFAC and other controllers can perform heavy truck platooning control tasks, the TD-cMFAC proposed in this invention exhibits superior tracking performance and speed control, as well as more precise control over the spacing between heavy trucks. Figure 6 As shown, when using a timed distance platooning strategy, the distance between heavy trucks increases with vehicle speed. Therefore, heavy truck platooning under TD-cMFAC control exhibits excellent lane-keeping capabilities, ensuring both orderly platooning and improved driving safety.

[0047] Table 3 RMS values ​​of heavy truck platooning control system Table 3 lists the root mean square (RMS) values ​​of the performance indicators for the heavy truck platooning system. The TD-cMFAC method shows lower RMS values ​​for all performance indicators compared to other methods, indicating that the TD-cMFAC controller performs better in terms of heavy truck platooning control accuracy. The GWO-PID controller parameters cannot be adaptively adjusted, while the IMFAC-TD controller, although capable of adaptive parameter adjustment, cannot simultaneously handle time delays and disturbances. The controller proposed in this invention achieves smoother platooning tracking control.

[0048] From a technical perspective, the TD-cMFAC scheme proposed in this invention has superior performance, mainly based on the following two points: 1) Compared with the GWO-PID controller, the TD-cMFAC controller can comprehensively consider time delay and system constraints, effectively suppressing system oscillations and instability; 2) Compared with the IMFAC-TD controller that uses compact form dynamic linearization (CFDL) technology, this invention captures the dynamic changes of historical data through partial form dynamic linearization technology, significantly improving the formation control accuracy.

[0049] Example 2 This embodiment provides an electronic device, which includes a processor and a memory communicatively connected to the processor; the memory stores instructions that are executed by the processor, and the instructions are executed by the processor to cause the processor to perform a model-free adaptive control method for multi-intelligent heavy truck formation according to Embodiment 1.

[0050] Example 3 A storage medium, which is a computer-readable storage medium, stores a computer program on the storage medium. When the computer program is executed by a processor, it implements a model-free adaptive control method for multi-intelligent heavy truck platooning as described in Embodiment 1.

[0051] The purpose of this invention is to address the vehicle input / output (I / O) data constraints (such as vehicle speed and acceleration limits) in practical longitudinal multi-vehicle cooperative platooning systems and their significant impact on control. A novel MFAC (Model-Free Adaptive Control) method is proposed to solve the longitudinal multi-vehicle cooperative platooning control problem. The MFAC scheme is a DDC (Data-Driven Control) method that only requires the input / output data of the controlled object, meaning that a specific vehicle model is no longer needed. Therefore, it is very convenient and practical and can be used on different vehicles. This method is geared towards SISO (Single-Input Single-Output) multi-agent systems (MAS), using the Partial Form Dynamic Linearization (PFDL) method to handle the system's dynamic characteristics and designing the controller based on the dynamic linearization model. Furthermore, by integrating a Smith predictor and a penalty function to constrain the input and output, a new TD-cMFAC (Model-Free Adaptive Control with Time Delay and ConstraintHandling) method is proposed, effectively solving the time delay and constraint handling problems in multi-vehicle systems.

[0052] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A model-free adaptive control method for multi-intelligent heavy truck platooning, characterized in that, Specifically, the steps include the following: S1, perform motion analysis on the heavy truck to obtain a nonlinear system; S2, Dynamic linearization of nonlinear systems, and design of TD-cMFAC controller based on time delay output prediction and input-output constraint processing; S3 uses the TD-cMFAC controller to control the heavy truck platoon.

2. The model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 1, characterized in that, In step S1, the vertical speed control dynamic system of the heavy truck is a discrete-time nonlinear system. （1）； in, Indicates the first The distance traveled by the heavy truck Indicates the first The acceleration of a heavy truck, Indicates time, Represents the time lag of a nonlinear system. Represents an unknown nonlinear function. and Let these represent the unknown input order and output order of the nonlinear system, respectively. This refers to the number of heavy trucks in the vehicle platoon.

3. The model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 1, characterized in that, Step S2 specifically includes the following steps: S2.1, Discrete-time nonlinear systems (1) satisfy the generalized Lipschitz condition, that is, for any time... ,have: （2）； Where, vector By sliding time window It consists of all the control inputs inside. A positive constant for the linearization length constant LLC. It is a positive number. The change in acceleration This represents the change in distance. S2.2, Discrete-time nonlinear system (1) has a time-varying vector called pseudo-gradient PG. This transforms the discrete-time nonlinear system (1) into a partially formatted dynamic linearized PFDL data model, as follows: （3）； in, ; ,and It is a positive number; For signal, for The transpose of, and at any time There are boundaries.

4. The model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 3, characterized in that, Step S2 also includes the following steps: S2.3, introducing the Smith estimation method, the dynamic linearization model is further transformed into: （4）； in, It is a differential signal.

5. The model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 4, characterized in that, Step S2 also includes the following steps: S2.4 uses graph theory to represent the communication and data transmission processes between vehicles, followers, and leaders: （5）； （6）； in, Indicates heavy truck , The communication status between them Indicates heavy truck The communication status between the facilitator and the guide; S2.5, considering the deviations between individual vehicles The definition is as follows: （7）； in, It is the expected trajectory. It is a heavy truck The actual output.

6. The model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 5, characterized in that, Step S2 also includes the following steps: S2.6, consider the following control input cost function : （8）； in, As a weighting factor, The desired distance; To concisely express the subsequent formulas, the following definitions are given: （9）； S2.7, Substituting formula (4) into formula (9) yields: （10）； in, and They represent loaded vehicles respectively. and A set; The control inputs satisfy the inherent physical constraints of the loaded vehicle platooning system: （11）； in, , These represent the lower and upper limits of allowed system input, respectively.

7. The model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 6, characterized in that, Step S2 also includes the following steps: S2.8, the constraint (11) is integrated into the original cost function (8) using a quadratic penalty function to obtain the augmented output cost function. : （12）； in, As a penalty factor, Let be a symmetric quadratic penalty function, defined as follows: （13）； in, This is a function to find the maximum value. S2.9 Substituting formula (10) into the augmented output cost function (12) and setting the derivative to zero, the constraint control law can be obtained, which is the final constraint TD-cMFAC control law. Represented as: （14）； in, Step size factor For the pseudo-partial derivative of the first heavy truck in the formation, for The estimated value, To control the input linearization length function, The constraint gradient term for the derivative of the penalty function: （15）。 8. A model-free adaptive control method for multi-intelligent heavy truck platooning according to claim 7, characterized in that, Step S2 also includes the following steps: S2.10, Establish the criterion function Estimating the pseudo gradient PG: （16）； in, The square of the norm; Selecting the optimal condition And using the matrix inverse lemma, the following results are obtained: （17）； in, for The estimated value; As a weighting factor, Step size factor; S2.11, using the reset algorithm to perform pseudo gradient estimation for heavy truck platooning: （18）； in, For positive integers, yes The first element, yes initial value, It is a symbolic function; S2.12, in order to obtain The delay output prediction TD is used, and the TD design is as follows: （19）； in, for The estimated value, for The estimated value, It is the discrete sampling step size. These are tracking parameters. These are filter parameters. This is the fastest control synthesis function; S2.13, when obtained After obtaining the estimated value of PG, the control law (14) is rewritten in the following form: （20）； （21）； in, Representing the The heavy truck receives the differential signal from TD. Representing the The heavy truck receives the differential signal from TD.

9. An electronic device, characterized in that, The electronic device includes a processor and a memory communicatively connected to the processor; the memory stores instructions that are executed by the processor to cause the processor to perform the model-free adaptive control method for multi-intelligent heavy truck platooning as described in any one of claims 1-8.

10. A storage medium, characterized in that, The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the model-free adaptive control method for multi-intelligent heavy truck formation as described in any one of claims 1-8.

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